# Geometric Surfaces

### Terms

Altitude of a Cone  -  The segment with one endpoint at the vertex of a cone and the other in the plane that contains the base of the cone.
Altitude of a Pyramid  -  The segment with one endpoint at the vertex of a pyramid and the other at the center of the base of the pyramid.
Base of a Cone  -  The simple closed curve that bounds part of the cone.
Base of a Cylinder  -  One of two simple closed curves that lie in parallel planes.
Base of a Prism  -  One of two polygons that lie in parallel planes.
Base of a Pyramid  -  A polygon that bounds part of the pyramid.
Center of a Sphere  -  The fixed point in the interior of a sphere from which all points on the sphere are equidistant
Circular Cone  -  A cone whose base is a circle
Circular Cylinder  -  A cylinder whose base is a circle.
Concave Simple Closed Surface  -  A simple closed surface in which one or more segments* drawn between points on the surface lie partially or wholly outside the surface.
Concentric Spheres  -  Spheres that share a common center.
Cone  -  A surface that includes a simple closed curve and the segments that join all the points on that curve with a single fixed point not in the plane of the curve.
Convex Simple Closed Surface  -  A simple closed curve in which a segment joining any two points on the surface lies entirely in the interior of the surface.
Cube  -  A regular polyhedron with six faces, all of which are congruent squares.
Cylinder  -  A geometric surface composed of two congruent simple closed curves lying in parallel planes and segments of parallel lines joining the curves.
Dodecahedron  -  A twelve-faced regular polyhedron whose faces are all congruent regular pentagons.
Edge  -  The intersection of two polygons in a polyhedron.
Face  -  A polygon in a polyhedron.
Geometric Solid  -  A region in space bounded by a closed surface.
Hemisphere  -  Exactly half of a sphere.
Isocahedron  -  A twenty-faced regular polyhedron whose faces are all congruent triangles.
Lateral Edge  -  An edge of a polyhedron, usually refers to a prism or a pyramid.
Lateral Face of a Prism  -  The parallelograms of a prism whose edges are the segments that connect the bases.
Lateral Face of a Pyramid  -  The triangles of a pyramid.
Lateral Surface of a Cone  -  The set of segments that join the base of a cone with its vertex.
Lateral Surface of a Cylinder  -  The set of segments that join the bases of a cylinder.
Octahedron  -  An eight-faced regular polyhedron whose faces are all congruent triangles.
Polyhedron  -  A simple closed surface composed of regions of intersecting planes--these regions are polygons
Prism  -  A polyhedron composed of two congruent polygons that lie in parallel planes and the segments that are part of parallel lines that join the congruent polygons.
Pyramid  -  A polyhedron composed of a polygon and the segments that join that polygon with a fixed point not in the plane of the polygon.
Radius of a Sphere  -  A segment with one endpoint at the center of a sphere and the other endpoint on the sphere.
Regular Polyhedron  -  A polyhedron whose faces are congruent regular polygons
Regular Pyramid  -  A pyramid whose base is a regular polygon and whose altitude intersects the plane of its base at the center of the base.
Right Circular Cone  -  A circular cone whose altitude intersects with the plane of the base at the center of the base.
Right Circular Cylinder  -  A circular cylinder whose lateral edges are perpendicular to the planes that contain the bases.
Right Prism  -  A prism whose lateral edges are perpendicular to the planes of the bases.
Simple Closed Surface  -  A surface that divides space into three distinct regions: 1) points in the interior of the surface, which always form the endpoints of finite segments; 2) points on the surface; and 3) points in the exterior of the surface, which can form the endpoints of infinite segments.
Sphere  -  A surface whose points all lie an equal distance from a fixed point in space.
Surface  -  A geometric figure that traces the motion of a curve in space. A surface is two-dimensional, but can span three dimensions.
Tetrahedron  -  A four-faced regular polyhedron whose faces are all congruent triangles.
Vertex of a Cone  -  The fixed point that is the endpoint of all the segments that form the lateral surface of a cone.
Vertex of a Polyhedron  -  Any point on a polyhedron that is the intersection of three or more faces.
Vertex of a Pyramid  -  The fixed point at the intersection of all the faces of the pyramid.

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