]> 2008/06/10 OpenCyc Knowledge Base Copyright© 2001-2008 Cycorp, Inc., http://www.cyc.com/, Austin, TX, USA This file contains an OWL representation of information contained in the OpenCyc Knowledge Base. The content of this OWL file is licensed under the Creative Commons Attribution 3.0 license whose text can be found at http://creativecommons.org/licenses/by/3.0/legalcode. The content of this OWL file, including the OpenCyc content it represents, constitutes the "Work" referred to in the Creative Commons license. The terms of this license equally apply to, without limitation, renamings and other logically equivalent reformulations of the content of this OWL file (or portions thereof) in any natural or formal language, as well as to derivations of this content or inclusion of it in other ontologies. externalID A unique, language-neutral, variable-sized identifier for a concept that can be used to refer unambiguously to that concept across OWL exports or across Cyc inference engines. label A natural-language representation for a concept that is both human readable and readable by the Cyc inference engine. These terms are not guaranteed to refer to the same concept across time but are guaranteed to be consistent within a particular OWL export. Use 'cycAnnot:externalID' for unambiguously referring to a concept across OWL exports or across Cyc inference engines. TwoDimensionalShapeType A specialization of #$SpatialThingTypeByGeometricShape (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPRuk5wpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalShapeType</a> is a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCpZwpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalGeometricThing</a> (q.v.). Instances include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rmSmWUM7yEdmAAAACs0uFOQ" class="cyc_term">Circle</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjVXJwpEbGdrcN5Y29ycA" class="cyc_term">Polygon</a>. Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPRuxZwpEbGdrcN5Y29ycA" class="cyc_term">ThreeDimensionalShapeType</a>. type of two dimensional shape types of two dimensional shape PolygonTypeByNumberOfSides type of polygon classified by number of sides A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPRuk5wpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalShapeType</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwTiY35wpEbGdrcN5Y29ycA" class="cyc_term">PolygonTypeByNumberOfSides</a> is the collection of all <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjVXJwpEbGdrcN5Y29ycA" class="cyc_term">Polygon</a>s (q.v.) that have the same particular number of sides (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvm9LU5wpEbGdrcN5Y29ycA" class="cyc_term">numberOfEdges</a>). Instances include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjrapwpEbGdrcN5Y29ycA" class="cyc_term">Triangle</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwM_725wpEbGdrcN5Y29ycA" class="cyc_term">Octagon</a>. Rhombus rhombus shaped thing A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rva60M5wpEbGdrcN5Y29ycA" class="cyc_term">Parallelogram</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwT9uHJwpEbGdrcN5Y29ycA" class="cyc_term">EquilateralPolygon</a> (qq.v.). This is the collection of all rhombi: four-sided polygons whose opposing sides are parallel and whose sides are all of equal length. A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rCl2_VFIuEdqAAAACs0uFOQ" class="cyc_term">Hemispheroid</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4ryStbyFITEdqAAAACs0uFOQ" class="cyc_term">Hemisphere</a> is a half- <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvgDAn5wpEbGdrcN5Y29ycA" class="cyc_term">Sphere</a>. Any great circle of a given sphere divides it into two hemispheres. See also <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPSJjZwpEbGdrcN5Y29ycA" class="cyc_term">HemisphericalSolid</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVj2hZwpEbGdrcN5Y29ycA" class="cyc_term">GeographicalHemisphere</a>. Note that, despite the latter collection's name, its instances do not approximate <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4ryStbyFITEdqAAAACs0uFOQ" class="cyc_term">Hemisphere</a>s as much as they do halves of oblate spheroids (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rCl2_VFIuEdqAAAACs0uFOQ" class="cyc_term">Hemispheroid</a>). hemisphere Hemisphere A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvn5lgpwpEbGdrcN5Y29ycA" class="cyc_term">Quadrilateral</a> (q.v.). A quadrilateral is an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r14l50Nk7EdmAAAAH6Q2cKw" class="cyc_term">CyclicQuadrilateral</a> if and only its vertices are concyclic (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r1BjHztk7EdmAAAAH6Q2cKw" class="cyc_term">concyclicPoints</a>): they all lie on a common <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rmSmWUM7yEdmAAAACs0uFOQ" class="cyc_term">Circle</a>. cyclic quadrilateral CyclicQuadrilateral half-plane HalfPlane A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCpZwpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalGeometricThing</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rW_U-PsyoEdmAAAACs0uFOQ" class="cyc_term">SurfaceRegion_SemiBounded</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViEeJwpEbGdrcN5Y29ycA" class="cyc_term">FlatSurfaceRegion</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvhDcyZwpEbGdrcN5Y29ycA" class="cyc_term">HalfPlane</a> is an semi-bounded portion of a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rN1T3Nlv9QdeJ7LFO9u6POw" class="cyc_term">Plane</a>, having a single straight line as a boundary. A straight line cuts any plane in which it lies into two half-planes. A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCpZwpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalGeometricThing</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rD_dw3OcvEdmAAAACs0uFOQ" class="cyc_term">CylindricalSurface</a> is the two-dimensional, non-planar, surface of a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwQBgIZwpEbGdrcN5Y29ycA" class="cyc_term">Cylinder</a> (q.v.). A cylindrical surface might be the entire surface (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r0li_0uQjEdmAAAACs6hO_g" class="cyc_term">boundaryOfSpatialThing</a>) of a finite cylinder (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rRBrT3kTOEdqAAAACs0uFOQ" class="cyc_term">CylindricalSurface_WithTopAndBottom</a>), or it might be just the tubular "side" surface of a finite or infinite cylinder (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r7ATwgkTLEdqAAAACs0uFOQ" class="cyc_term">CylindricalSurface_WithoutTopAndBottom</a>). Note that, in the case of an infinitely long cylinder with no top or bottom, the side surface is the entire surface. CylindricalSurface cylindrical surface CylindricalSurface-WithoutTopAndBottom cylindrical surface with no top or bottom A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rD_dw3OcvEdmAAAACs0uFOQ" class="cyc_term">CylindricalSurface</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwQBgy5wpEbGdrcN5Y29ycA" class="cyc_term">Tube</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r7ATwgkTLEdqAAAACs0uFOQ" class="cyc_term">CylindricalSurface_WithoutTopAndBottom</a> is the two-dimensional, non-planar, tubelike "side" surface of a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwQBgIZwpEbGdrcN5Y29ycA" class="cyc_term">Cylinder</a> (q.v.). Note that a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r7ATwgkTLEdqAAAACs0uFOQ" class="cyc_term">CylindricalSurface_WithoutTopAndBottom</a> (like the cylinder it is the side of) might be finite or infinite in height. If finite, it will be a proper part of some <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rRBrT3kTOEdqAAAACs0uFOQ" class="cyc_term">CylindricalSurface_WithTopAndBottom</a> (q.v.). PolyhedralSurface polyhedral surface A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCpZwpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalGeometricThing</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwD6uDJwpEbGdrcN5Y29ycA" class="cyc_term">SurfaceRegion_Unbounded</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rCF6xbM1pEdmAAAACs0uFOQ" class="cyc_term">SurfaceRegion_Finite</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rQfyHuOgnEdmAAAACs0uFOQ" class="cyc_term">PolyhedralSurface</a> is the two-dimensional, non-planar, unbounded surface of a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvtjhbpwpEbGdrcN5Y29ycA" class="cyc_term">Polyhedron</a> (q.v.); it is the spatial sum of several (i.e. four or more) <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjVXJwpEbGdrcN5Y29ycA" class="cyc_term">Polygon</a>s. ConicalSurface conical surface A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCpZwpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalGeometricThing</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvZWBA5wpEbGdrcN5Y29ycA" class="cyc_term">SurfaceRegion</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rcTGCWOdWEdmAAAACs0uFOQ" class="cyc_term">ConicalSurface</a> is either (i) the entire two-dimensional, non-planar, unbounded surface of a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwQwzSJwpEbGdrcN5Y29ycA" class="cyc_term">Cone</a> (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rcrKOqkGYEdqAAAACs0uFOQ" class="cyc_term">ConicalSurface_WithBase</a>) or (ii) the same, but without the circular base (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rYHkUMkGaEdqAAAACs0uFOQ" class="cyc_term">ConicalSurface_WithoutBase</a>). A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviHxm5wpEbGdrcN5Y29ycA" class="cyc_term">PlaneFigure</a> (q.v.). This is the collection of all semi-circular two-dimensional space regions. Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwI0rpZwpEbGdrcN5Y29ycA" class="cyc_term">SemicircularRegion</a> is half of a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCZZwpEbGdrcN5Y29ycA" class="cyc_term">CircularRegion</a>. semicircle SemicircularRegion Spheroid spheroid A <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPRuk5wpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalShapeType</a> and a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv9CgZpwpEbGdrcN5Y29ycA" class="cyc_term">Ellipsoid</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rzCm-HubNQdaO7ZipW2UPxw" class="cyc_term">Spheroid</a> is an ellipsoid that has two axes (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r4BM6CvVqEdmAAAACs0uFOQ" class="cyc_term">symmetricAxes</a>) of equal length (if all of an ellipsoid's axes are of equal length, it is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvgDAn5wpEbGdrcN5Y29ycA" class="cyc_term">Sphere</a>). With respect to a non-spherical spheroid, the axes that are of equal length are equatorial axes, and an axis that is perpendicular to an equatorial axis is a polar axis. (Since a non-spherical spheroid's equatorial axes are coplanar, it therefore has a unique polar axis.) A spheroid whose equatorial axes are longer than its polar axis is an <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rQVBN3ve_EdmAAAACs0uFOQ" class="cyc_term">OblateSpheroid</a>, and one whose polar axis is longer than its equatorial axes is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHAo0yveyEdmAAAACs0uFOQ" class="cyc_term">ProlateSpheroid</a>. See also <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r_8mo2PlOEdmAAAACs0uFOQ" class="cyc_term">polarRadiusOfSpheroid</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rbuaGTPlJEdmAAAACs0uFOQ" class="cyc_term">equatorialRadiusOfSpheroid</a>. Note that, since an axis is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjC4JwpEbGdrcN5Y29ycA" class="cyc_term">Line_Straight</a>, it strictly speaking has infinite length. So when we say that a given axis <code>AXIS</code> of a spheroid <code>SPHEROID</code> has the length <code>LENGTH</code>, it is really shorthand for saying that the line-segment part of <code>AXIS</code> whose endpoints are where <code>AXIS</code> intersects <code>SPHEROID</code> has <code>LENGTH</code>. RightTriangle right triangle A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjrapwpEbGdrcN5Y29ycA" class="cyc_term">Triangle</a> (q.v.). This is the collection of all triangles having two adjacent sides that form a right (i.e. 90 degree) angle. A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rQfyHuOgnEdmAAAACs0uFOQ" class="cyc_term">PolyhedralSurface</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rV3DKPum_EdmAAAACs0uFOQ" class="cyc_term">WedgeSurface</a> is the two-dimensional, non-planar, unbounded surface of a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwTr58ZwpEbGdrcN5Y29ycA" class="cyc_term">Wedge</a> (q.v.); it is the spatial sum of five flat externally-connected polygons, two of which are (mutually-congruent) <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjrapwpEbGdrcN5Y29ycA" class="cyc_term">Triangle</a>s and three of which are <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjUl5wpEbGdrcN5Y29ycA" class="cyc_term">Rectangle</a>s. WedgeSurface wedge surface oval A specialization of both <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviHxm5wpEbGdrcN5Y29ycA" class="cyc_term">PlaneFigure</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwQBfkZwpEbGdrcN5Y29ycA" class="cyc_term">RoundObject</a> (qq.v.). This is the collection of all two-dimensional space regions whose boundaries are <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rKAYkmM7jEdmAAAACs0uFOQ" class="cyc_term">Ellipse</a>s (q.v.). Geometrically, an elliptical region is an two-dimensional region bounded by a closed curve that is the path of a point that moves so that the sum of its distances from two fixed points (called "foci") is constant. An important specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv2v6GZwpEbGdrcN5Y29ycA" class="cyc_term">EllipticalRegion</a> is <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCZZwpEbGdrcN5Y29ycA" class="cyc_term">CircularRegion</a>, the collection of elliptical regions such that the distance between their boundaries' two foci is zero. Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv9CgZpwpEbGdrcN5Y29ycA" class="cyc_term">Ellipsoid</a>. EllipticalRegion geometric plane Plane A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCpZwpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalGeometricThing</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwD6uDJwpEbGdrcN5Y29ycA" class="cyc_term">SurfaceRegion_Unbounded</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViEeJwpEbGdrcN5Y29ycA" class="cyc_term">FlatSurfaceRegion</a> (qq.v.). This is the collection of all geometric planes. Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rN1T3Nlv9QdeJ7LFO9u6POw" class="cyc_term">Plane</a> is an unbounded, perfectly flat, two-dimensional region of space. See also <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvhDcyZwpEbGdrcN5Y29ycA" class="cyc_term">HalfPlane</a>. A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjUl5wpEbGdrcN5Y29ycA" class="cyc_term">Rectangle</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwE_puZwpEbGdrcN5Y29ycA" class="cyc_term">Rhombus</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvyHrCJwpEbGdrcN5Y29ycA" class="cyc_term">RegularPolygon</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjUVZwpEbGdrcN5Y29ycA" class="cyc_term">Square</a> is a four-sided polygon whose sides are all of equal length and whose internal angles are all of equal measure (viz. 90 degrees). square Square A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHph1GumuEdmAAAACs0uFOQ" class="cyc_term">RectangularParallelepipedSurface</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rKlYAoOmwEdmAAAACs0uFOQ" class="cyc_term">CubicalSurface</a> is the two-dimensional, non-planar, unbounded surface of a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwP4qT5wpEbGdrcN5Y29ycA" class="cyc_term">Cube</a> (q.v.); it is the spatial sum of six <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjUVZwpEbGdrcN5Y29ycA" class="cyc_term">Square</a>s that are edge-connected at right angles. CubicalSurface cubical surface A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviHxm5wpEbGdrcN5Y29ycA" class="cyc_term">PlaneFigure</a> and #$ConnectedSpaceRegion (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjVXJwpEbGdrcN5Y29ycA" class="cyc_term">Polygon</a> is a plane figure whose boundary is one or more closed curves, each consisting of three or more straight line-segments joined end-to-end (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvoMjlpwpEbGdrcN5Y29ycA" class="cyc_term">LineString</a>). Specializations of this collection include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjrapwpEbGdrcN5Y29ycA" class="cyc_term">Triangle</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv8EXxJwpEbGdrcN5Y29ycA" class="cyc_term">Hexagon</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvyHrCJwpEbGdrcN5Y29ycA" class="cyc_term">RegularPolygon</a>. See also <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwTiY35wpEbGdrcN5Y29ycA" class="cyc_term">PolygonTypeByNumberOfSides</a>. polygon Polygon ProlateSpheroid A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rzCm-HubNQdaO7ZipW2UPxw" class="cyc_term">Spheroid</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHAo0yveyEdmAAAACs0uFOQ" class="cyc_term">ProlateSpheroid</a> is a "pointy" spheroid: one whose polar radius is greater than its equatorial radius (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r_8mo2PlOEdmAAAACs0uFOQ" class="cyc_term">polarRadiusOfSpheroid</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rbuaGTPlJEdmAAAACs0uFOQ" class="cyc_term">equatorialRadiusOfSpheroid</a>). Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rQVBN3ve_EdmAAAACs0uFOQ" class="cyc_term">OblateSpheroid</a>. prolate spheroid A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rva60M5wpEbGdrcN5Y29ycA" class="cyc_term">Parallelogram</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwEAWf5wpEbGdrcN5Y29ycA" class="cyc_term">Rhomboid</a> is a four-sided polygon whose opposing sides are parallel and whose adjacent sides are of unequal length. Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwE_puZwpEbGdrcN5Y29ycA" class="cyc_term">Rhombus</a>. rhomboid Rhomboid A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rqw3eMFIyEdqAAAACs0uFOQ" class="cyc_term">Hemiellipsoid</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rCl2_VFIuEdqAAAACs0uFOQ" class="cyc_term">Hemispheroid</a> is a half- <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rzCm-HubNQdaO7ZipW2UPxw" class="cyc_term">Spheroid</a>. Any great ellipse of a given spheroid (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rcZbvmlIhEdqAAAACs0uFOQ" class="cyc_term">greatEllipseOfSpheroid</a>) divides it into two hemispheroids. Note that, despite the collection's name, instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVj2hZwpEbGdrcN5Y29ycA" class="cyc_term">GeographicalHemisphere</a> do not approximate <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4ryStbyFITEdqAAAACs0uFOQ" class="cyc_term">Hemisphere</a>s (cf.) as much as they do <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rCl2_VFIuEdqAAAACs0uFOQ" class="cyc_term">Hemispheroid</a>s. hemispheroid Hemispheroid (RegularPolygonTypeFn Quadrilateral) square CyclicPolygon cyclic polygon A <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rN8XS8P9zEdmAAAACs6hO_g" class="cyc_term">CyclicPolygon</a> is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjVXJwpEbGdrcN5Y29ycA" class="cyc_term">Polygon</a> whose vertices all lie on a common <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rmSmWUM7yEdmAAAACs0uFOQ" class="cyc_term">Circle</a>. Every <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvyHrCJwpEbGdrcN5Y29ycA" class="cyc_term">RegularPolygon</a> is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rN8XS8P9zEdmAAAACs6hO_g" class="cyc_term">CyclicPolygon</a>. Since three noncolinear points determine a unique <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rmSmWUM7yEdmAAAACs0uFOQ" class="cyc_term">Circle</a>, every <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjrapwpEbGdrcN5Y29ycA" class="cyc_term">Triangle</a> is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rN8XS8P9zEdmAAAACs6hO_g" class="cyc_term">CyclicPolygon</a> as well. geometrical plane figure PlaneFigure A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvpHwrZwpEbGdrcN5Y29ycA" class="cyc_term">GeometricFigure</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCpZwpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalGeometricThing</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvYyzApwpEbGdrcN5Y29ycA" class="cyc_term">SurfaceRegion_Bounded</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViEeJwpEbGdrcN5Y29ycA" class="cyc_term">FlatSurfaceRegion</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviHxm5wpEbGdrcN5Y29ycA" class="cyc_term">PlaneFigure</a> is an intangible, self-connected, bounded, two-dimensional, geometrical figure that can be embedded in a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rN1T3Nlv9QdeJ7LFO9u6POw" class="cyc_term">Plane</a>. Specializations of this collection include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjVXJwpEbGdrcN5Y29ycA" class="cyc_term">Polygon</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCZZwpEbGdrcN5Y29ycA" class="cyc_term">CircularRegion</a>. Note that the boundary of a plane figure is not itself an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviHxm5wpEbGdrcN5Y29ycA" class="cyc_term">PlaneFigure</a>, but is rather a one-dimensional, planar, closed curve (see e.g. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rmSmWUM7yEdmAAAACs0uFOQ" class="cyc_term">Circle</a>). A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rva60M5wpEbGdrcN5Y29ycA" class="cyc_term">Parallelogram</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviCcIZwpEbGdrcN5Y29ycA" class="cyc_term">EquiangularPolygon</a>. This is the collection of all rectangles: four-sided polygons whose opposing sides are parallel and whose internal angles are all of equal measure (viz. 90 degrees). Rectangle rectangle rectangular parallelepiped surface A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r5SIsCujzEdmAAAACs0uFOQ" class="cyc_term">ParallelepipedSurface</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHph1GumuEdmAAAACs0uFOQ" class="cyc_term">RectangularParallelepipedSurface</a> is the two-dimensional, non-planar, unbounded surface of a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPua9pwpEbGdrcN5Y29ycA" class="cyc_term">RectangularParallelepiped</a> (q.v.); it is the spatial sum of six <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjUl5wpEbGdrcN5Y29ycA" class="cyc_term">Rectangle</a>s that are edge-connected at right angles. RectangularParallelepipedSurface the union of { prolate spheroids, oblate spheroids } ProperSpheroid A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rzCm-HubNQdaO7ZipW2UPxw" class="cyc_term">Spheroid</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4ruiS-VFIrEdqAAAACs0uFOQ" class="cyc_term">ProperSpheroid</a> is a spheroid that is not a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvgDAn5wpEbGdrcN5Y29ycA" class="cyc_term">Sphere</a>. Thus its polar radius is different than its equatorial radius (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r_8mo2PlOEdmAAAACs0uFOQ" class="cyc_term">polarRadiusOfSpheroid</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rbuaGTPlJEdmAAAACs0uFOQ" class="cyc_term">equatorialRadiusOfSpheroid</a>). If its polar radius is longer it's a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHAo0yveyEdmAAAACs0uFOQ" class="cyc_term">ProlateSpheroid</a>; if its equatorial radius is longer it's an <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rQVBN3ve_EdmAAAACs0uFOQ" class="cyc_term">OblateSpheroid</a>. CircularRegion A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv2v6GZwpEbGdrcN5Y29ycA" class="cyc_term">EllipticalRegion</a> (q.v.). This is the collection of elliptical regions whose boundaries are <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rmSmWUM7yEdmAAAACs0uFOQ" class="cyc_term">Circle</a>s. Geometrically, a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCZZwpEbGdrcN5Y29ycA" class="cyc_term">CircularRegion</a> is a plane figure bounded by a closed curve each point on which is equidistant from a single ("center") point. Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPuen5wpEbGdrcN5Y29ycA" class="cyc_term">Disc</a>. circle A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCpZwpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalGeometricThing</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvYyzApwpEbGdrcN5Y29ycA" class="cyc_term">SurfaceRegion_Bounded</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rCF6xbM1pEdmAAAACs0uFOQ" class="cyc_term">SurfaceRegion_Finite</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rqw3eMFIyEdqAAAACs0uFOQ" class="cyc_term">Hemiellipsoid</a> is a half- <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv9CgZpwpEbGdrcN5Y29ycA" class="cyc_term">Ellipsoid</a>. Any great ellipse of a given ellipsoid (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r1xtToFInEdqAAAACs0uFOQ" class="cyc_term">greatEllipseOfEllipsoid</a>) divides it into two hemiellipsoids. hemiellipsoid Hemiellipsoid sphere A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rzCm-HubNQdaO7ZipW2UPxw" class="cyc_term">Spheroid</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvgDAn5wpEbGdrcN5Y29ycA" class="cyc_term">Sphere</a> is a two-dimensional unbounded surface, embedded in a three-dimensional space, and such that each point on it is equidistant from some given point. See also <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r3iex1N9UEdmAAAACs0uFOQ" class="cyc_term">SphericalSolid</a>, each instance of which is an (intangible or tangible) three-dimensional object whose boundary is or approximates a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvgDAn5wpEbGdrcN5Y29ycA" class="cyc_term">Sphere</a>. Sphere CylindricalSurface-WithTopAndBottom cylindrical surface with top and bottom A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rD_dw3OcvEdmAAAACs0uFOQ" class="cyc_term">CylindricalSurface</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rylUGus4bEdmAAAACs0uFOQ" class="cyc_term">ClosedSurfaceRegion</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rRBrT3kTOEdqAAAACs0uFOQ" class="cyc_term">CylindricalSurface_WithTopAndBottom</a> is the entire two-dimensional surface of a finite <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwQBgIZwpEbGdrcN5Y29ycA" class="cyc_term">Cylinder</a> (q.v.). Note that each <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rRBrT3kTOEdqAAAACs0uFOQ" class="cyc_term">CylindricalSurface_WithTopAndBottom</a> has as proper parts a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r7ATwgkTLEdqAAAACs0uFOQ" class="cyc_term">CylindricalSurface_WithoutTopAndBottom</a> (q.v.) and two <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCZZwpEbGdrcN5Y29ycA" class="cyc_term">CircularRegion</a>s. A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjVXJwpEbGdrcN5Y29ycA" class="cyc_term">Polygon</a>. This is the collection of all two-dimensional polygons that are both <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviCcIZwpEbGdrcN5Y29ycA" class="cyc_term">EquiangularPolygon</a>s and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwT9uHJwpEbGdrcN5Y29ycA" class="cyc_term">EquilateralPolygon</a>s (qq.v.). One specialization of this collection is <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjUVZwpEbGdrcN5Y29ycA" class="cyc_term">Square</a>. See also <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rRGAb3F4nQdeYVca9lNCZDw" class="cyc_term">RegularPolygonTypeFn</a>. regular polygon RegularPolygon A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rQfyHuOgnEdmAAAACs0uFOQ" class="cyc_term">PolyhedralSurface</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rTz2RxOm8EdmAAAACs0uFOQ" class="cyc_term">PyramidalSurface</a> is the two-dimensional, non-planar, unbounded surface of a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjJX5wpEbGdrcN5Y29ycA" class="cyc_term">Pyramid</a> (q.v.); it is the spatial sum of an n-sided polygon that is its base with n-1 triangles that meet at a common vertex. PyramidalSurface pyramidal surface torus surface A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCpZwpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalGeometricThing</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwD6uDJwpEbGdrcN5Y29ycA" class="cyc_term">SurfaceRegion_Unbounded</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rCF6xbM1pEdmAAAACs0uFOQ" class="cyc_term">SurfaceRegion_Finite</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rasrS8OjyEdmAAAACs0uFOQ" class="cyc_term">TorusSurface</a> is the two-dimensional, non-planar, unbounded surface of a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4ryO43AFsjQdeAPO4LYlJlgA" class="cyc_term">Torus</a> (q.v.). TorusSurface Ellipsoid ellipsoid A specialization of both <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwQBfkZwpEbGdrcN5Y29ycA" class="cyc_term">RoundObject</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCpZwpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalGeometricThing</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rylUGus4bEdmAAAACs0uFOQ" class="cyc_term">ClosedSurfaceRegion</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv9CgZpwpEbGdrcN5Y29ycA" class="cyc_term">Ellipsoid</a> is a two-dimensional unbounded surface, embedded in a three-dimensional space, and such that the planar sections along its respective internal axes are <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rKAYkmM7jEdmAAAACs0uFOQ" class="cyc_term">Ellipse</a>s (q.v.). Note that <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvgDAn5wpEbGdrcN5Y29ycA" class="cyc_term">Sphere</a> and its generalization <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rzCm-HubNQdaO7ZipW2UPxw" class="cyc_term">Spheroid</a> are specializations of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv9CgZpwpEbGdrcN5Y29ycA" class="cyc_term">Ellipsoid</a>. See also <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rZFRl6N9NEdmAAAACs0uFOQ" class="cyc_term">EllipsoidalSolid</a>, each instance of which is an (intangible or tangible) three-dimensional object whose boundary is or approximates an <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv9CgZpwpEbGdrcN5Y29ycA" class="cyc_term">Ellipsoid</a>. Parallelogram parallelogram A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvn5lgpwpEbGdrcN5Y29ycA" class="cyc_term">Quadrilateral</a> (q.v.). This is the collection of all four-sided polygons such that each side is parallel to its opposite side. Specializations of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rva60M5wpEbGdrcN5Y29ycA" class="cyc_term">Parallelogram</a> include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjUl5wpEbGdrcN5Y29ycA" class="cyc_term">Rectangle</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwE_puZwpEbGdrcN5Y29ycA" class="cyc_term">Rhombus</a>. A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rcTGCWOdWEdmAAAACs0uFOQ" class="cyc_term">ConicalSurface</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwD6uDJwpEbGdrcN5Y29ycA" class="cyc_term">SurfaceRegion_Unbounded</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rCF6xbM1pEdmAAAACs0uFOQ" class="cyc_term">SurfaceRegion_Finite</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rcrKOqkGYEdqAAAACs0uFOQ" class="cyc_term">ConicalSurface_WithBase</a> is the entire two-dimensional, non-planar, unbounded surface of a finite <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwQwzSJwpEbGdrcN5Y29ycA" class="cyc_term">Cone</a> (q.v.). It is the unbounded sum of a finite <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rYHkUMkGaEdqAAAACs0uFOQ" class="cyc_term">ConicalSurface_WithoutBase</a> (cf.) and a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCZZwpEbGdrcN5Y29ycA" class="cyc_term">CircularRegion</a> (i.e. the base). ConicalSurface-WithBase conical surface with a base A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rzCm-HubNQdaO7ZipW2UPxw" class="cyc_term">Spheroid</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rQVBN3ve_EdmAAAACs0uFOQ" class="cyc_term">OblateSpheroid</a> is a "squashed" spheroid: one whose polar radius is less than its equatorial radius (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r_8mo2PlOEdmAAAACs0uFOQ" class="cyc_term">polarRadiusOfSpheroid</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rbuaGTPlJEdmAAAACs0uFOQ" class="cyc_term">equatorialRadiusOfSpheroid</a>). Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHAo0yveyEdmAAAACs0uFOQ" class="cyc_term">ProlateSpheroid</a>. OblateSpheroid oblate spheroid A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjVXJwpEbGdrcN5Y29ycA" class="cyc_term">Polygon</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwT9uHJwpEbGdrcN5Y29ycA" class="cyc_term">EquilateralPolygon</a> is a polygon whose sides are all of equal length. See also <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviCcIZwpEbGdrcN5Y29ycA" class="cyc_term">EquiangularPolygon</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvyHrCJwpEbGdrcN5Y29ycA" class="cyc_term">RegularPolygon</a>. equilateral shaped thing EquilateralPolygon A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvn5lgpwpEbGdrcN5Y29ycA" class="cyc_term">Quadrilateral</a> (q.v.). A <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvxNWBJwpEbGdrcN5Y29ycA" class="cyc_term">Trapezoid</a> is a four-sided polygon that has exactly two parallel sides. trapezoid Trapezoid A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rcTGCWOdWEdmAAAACs0uFOQ" class="cyc_term">ConicalSurface</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rYHkUMkGaEdqAAAACs0uFOQ" class="cyc_term">ConicalSurface_WithoutBase</a> is the two-dimensional, non-planar, surface of a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwQwzSJwpEbGdrcN5Y29ycA" class="cyc_term">Cone</a> (q.v.) minus the base (cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rcrKOqkGYEdqAAAACs0uFOQ" class="cyc_term">ConicalSurface_WithBase</a>). The entire surface of an infinite cone is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rYHkUMkGaEdqAAAACs0uFOQ" class="cyc_term">ConicalSurface_WithoutBase</a>. conical surface without a base ConicalSurface-WithoutBase EquiangularPolygon equiangular thing A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjVXJwpEbGdrcN5Y29ycA" class="cyc_term">Polygon</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviCcIZwpEbGdrcN5Y29ycA" class="cyc_term">EquiangularPolygon</a> is a polygon whose internal angles are all of equal measure. See also <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwT9uHJwpEbGdrcN5Y29ycA" class="cyc_term">EquilateralPolygon</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvyHrCJwpEbGdrcN5Y29ycA" class="cyc_term">RegularPolygon</a>. ParallelepipedSurface parallelepiped surface A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rQfyHuOgnEdmAAAACs0uFOQ" class="cyc_term">PolyhedralSurface</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r5SIsCujzEdmAAAACs0uFOQ" class="cyc_term">ParallelepipedSurface</a> is the two-dimensional, non-planar, unbounded surface of a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rzFfAWlQWQdeD1q0iNpVklw" class="cyc_term">Parallelepiped</a> (q.v.); it is the spatial sum of six externally-connected <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rva60M5wpEbGdrcN5Y29ycA" class="cyc_term">Parallelogram</a>s. The collection of all specializations of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHIBS0h_TEdaAAABQ2rksLw" class="cyc_term">FirstOrderCollection</a>, that is, of all collections of (first-order) collections, and an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHUFI8h_TEdaAAABQ2rksLw" class="cyc_term">ThirdOrderCollection</a>. Instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHQdVmB_TEdaAAABQ2rksLw" class="cyc_term">SecondOrderCollection</a> are collections of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHIBS0h_TEdaAAABQ2rksLw" class="cyc_term">FirstOrderCollection</a>s. Any instance of any instance of any instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHQdVmB_TEdaAAABQ2rksLw" class="cyc_term">SecondOrderCollection</a> is an <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaApwpEbGdrcN5Y29ycA" class="cyc_term">Individual</a>. SecondOrderCollection second-order Cyc collection A <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rtGXkHpNaEdqAAAACs0uFOQ" class="cyc_term">KBDependentCollection</a> of collections of collections (and thus an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviPYH5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionTypeType</a> and a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvtppU5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionType</a>). A sibling-disjoint collection type is such that its known (i.e. KB-represented) instances are collections that -- save for any that are related to each other by <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBDpwpEbGdrcN5Y29ycA" class="cyc_term">genls</a> and any that are explicitly asserted to be exceptions (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwQtVmpwpEbGdrcN5Y29ycA" class="cyc_term">siblingDisjointExceptions</a>) -- are disjoint from each other. More precisely, each instance <code>SIB</code> of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA4pwpEbGdrcN5Y29ycA" class="cyc_term">SiblingDisjointCollectionType</a> is a collection of collections that has the following KB-dependent property: For any two known instances <code>COL1</code> and <code>COL2</code> of <code>SIB</code>, at least one of the following is known to hold: <pre> (a) (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBDpwpEbGdrcN5Y29ycA" class="cyc_term">genls</a> COL1 COL2) (b) (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBDpwpEbGdrcN5Y29ycA" class="cyc_term">genls</a> COL2 COL1) (c) (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwQtVmpwpEbGdrcN5Y29ycA" class="cyc_term">siblingDisjointExceptions</a> COL1 COL2) (d) (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA45wpEbGdrcN5Y29ycA" class="cyc_term">disjointWith</a> COL1 COL2) </pre> Moreover, note that if <code>MT</code> is a context (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA1ZwpEbGdrcN5Y29ycA" class="cyc_term">Microtheory</a>) in which (i) both <code>(<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBBJwpEbGdrcN5Y29ycA" class="cyc_term">isa</a> COL1 SIB)</code> and <code>(<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBBJwpEbGdrcN5Y29ycA" class="cyc_term">isa</a> COL2 SIB)</code> hold and (ii) neither <code>(<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBDpwpEbGdrcN5Y29ycA" class="cyc_term">genls</a> COL1 COL2)</code> nor <code>(<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBDpwpEbGdrcN5Y29ycA" class="cyc_term">genls</a> COL2 COL1)</code> nor <code>(<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwQtVmpwpEbGdrcN5Y29ycA" class="cyc_term">siblingDisjointExceptions</a> COL1 COL2)</code> is known to hold (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwP-JvpwpEbGdrcN5Y29ycA" class="cyc_term">knownSentence</a>), then <code>(<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA45wpEbGdrcN5Y29ycA" class="cyc_term">disjointWith</a> COL1 COL2)</code> holds by default in <code>MT</code>. For example, in <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjakJwpEbGdrcN5Y29ycA" class="cyc_term">BiologyMt</a> both <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAkpwpEbGdrcN5Y29ycA" class="cyc_term">Person</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaoJwpEbGdrcN5Y29ycA" class="cyc_term">Dog</a> are instances of the sibling-disjoint collection type <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjK65wpEbGdrcN5Y29ycA" class="cyc_term">BiologicalSpecies</a>, while neither (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBDpwpEbGdrcN5Y29ycA" class="cyc_term">genls</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAkpwpEbGdrcN5Y29ycA" class="cyc_term">Person</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaoJwpEbGdrcN5Y29ycA" class="cyc_term">Dog</a>) nor (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBDpwpEbGdrcN5Y29ycA" class="cyc_term">genls</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaoJwpEbGdrcN5Y29ycA" class="cyc_term">Dog</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAkpwpEbGdrcN5Y29ycA" class="cyc_term">Person</a>) nor (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwQtVmpwpEbGdrcN5Y29ycA" class="cyc_term">siblingDisjointExceptions</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAkpwpEbGdrcN5Y29ycA" class="cyc_term">Person</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaoJwpEbGdrcN5Y29ycA" class="cyc_term">Dog</a>) is known to hold in that context; consequently, (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA45wpEbGdrcN5Y29ycA" class="cyc_term">disjointWith</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAkpwpEbGdrcN5Y29ycA" class="cyc_term">Person</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaoJwpEbGdrcN5Y29ycA" class="cyc_term">Dog</a>) holds by default in <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjakJwpEbGdrcN5Y29ycA" class="cyc_term">BiologyMt</a>. Instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA4pwpEbGdrcN5Y29ycA" class="cyc_term">SiblingDisjointCollectionType</a> include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVji6JwpEbGdrcN5Y29ycA" class="cyc_term">BiologicalTaxon</a> (and its specializations), <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwKTnSJwpEbGdrcN5Y29ycA" class="cyc_term">OrganismPartType</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwE01SZwpEbGdrcN5Y29ycA" class="cyc_term">RelationshipTypeByArity</a>. See the generalization <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rk8dxOFcGEdaLwgACs0uFOQ" class="cyc_term">SiblingDisjointSetOrCollectionType</a>. Also cf. the stronger notion of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvWPoRpwpEbGdrcN5Y29ycA" class="cyc_term">DisjointCollectionType</a>. sibling disjoint collection type SiblingDisjointCollectionType Pretty String (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwLSVCpwpEbGdrcN5Y29ycA" class="cyc_term">prettyString</a> TERM STRING) means that STRING is the English word or expression (sequence of words) commonly used to refer to TERM. The predicate <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwLSVCpwpEbGdrcN5Y29ycA" class="cyc_term">prettyString</a> is used by the code which generates CycL to English paraphrases, but its applicability is not restricted to this use. prettyString TwoDimensionalShapeType A specialization of #$SpatialThingTypeByGeometricShape (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPRuk5wpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalShapeType</a> is a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCpZwpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalGeometricThing</a> (q.v.). Instances include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rmSmWUM7yEdmAAAACs0uFOQ" class="cyc_term">Circle</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjVXJwpEbGdrcN5Y29ycA" class="cyc_term">Polygon</a>. Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPRuxZwpEbGdrcN5Y29ycA" class="cyc_term">ThreeDimensionalShapeType</a>. type of two dimensional shape Shape-Spatial-Topic shape-spatial-topic type of shape A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPRuD5wpEbGdrcN5Y29ycA" class="cyc_term">SpatialThingTypeByShape</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwU-SlZwpEbGdrcN5Y29ycA" class="cyc_term">GeometricShapeType</a> is a type of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjELpwpEbGdrcN5Y29ycA" class="cyc_term">GeometricallyDescribableThing</a> (q.v.) whose own instances are all and only those things that have a common shape that is characterizable in relatively simple geometric terms. An instance of a given geometric shape-type is a geometrically-describable object, which might either be intangible or tangible (though in the latter case it must be three-dimensional). For example, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvgDAn5wpEbGdrcN5Y29ycA" class="cyc_term">Sphere</a> is the collection of all spherical object; it includes both spherical space regions and crystal balls. Similarly, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rmSmWUM7yEdmAAAACs0uFOQ" class="cyc_term">Circle</a> is the collection of all two-dimensional circles; all of its instances are intangible, since tangible objects are by their nature three-dimensional. Specializations of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwU-SlZwpEbGdrcN5Y29ycA" class="cyc_term">GeometricShapeType</a> include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPRuk5wpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalShapeType</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPRuxZwpEbGdrcN5Y29ycA" class="cyc_term">ThreeDimensionalShapeType</a>. GeometricShapeType TwoDimensionalShapeType A specialization of #$SpatialThingTypeByGeometricShape (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPRuk5wpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalShapeType</a> is a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjCpZwpEbGdrcN5Y29ycA" class="cyc_term">TwoDimensionalGeometricThing</a> (q.v.). Instances include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rmSmWUM7yEdmAAAACs0uFOQ" class="cyc_term">Circle</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjVXJwpEbGdrcN5Y29ycA" class="cyc_term">Polygon</a>. Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPRuxZwpEbGdrcN5Y29ycA" class="cyc_term">ThreeDimensionalShapeType</a>. type of two dimensional shape