Prismatoid
From Free net encyclopedia
A prismatoid is a polyhedron where all vertices lie in two parallel planes. Under some circumstances it is called a prismoid (if both planes have the same number of elements.)
Image:Pentagonal pyramid.png Image:Pentagonal prism.png Image:Pentagonal antiprism.png Image:Pentagrammic crossed-antiprism.png Image:Pentagonal cupola.png Image:Pentagonal frustum.png
Families of prismatoids include:
- Pyramids, where one plane contains only a single point;
- Wedges, where one plane contains only two points;
- Prisms, where the polygons in each plane are congruent and joined by rectangles or parallelograms;
- Antiprisms, where the polygons in each plane are congruent and joined by an alternating strip of triangles;
- crossed-Antiprisms;
- Cupolas, where the polygon in one plane contains twice as many points as the other and is joined to it by alternating triangles and rectangles;
- Frustum obtained by truncation of a pyramid;
- Quadrilateral-faced hexahedral prismatoids:
- Parallelepiped - six parallelogram faces
- Rhombohedron - six rhombi faces
- Hexahedral trapezohedron - six congruent rhombi faces
- Cuboid - six rectangular faces
- Quadrilateral frustum - an apex-truncated square pyramid
- Cube - six square faces
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