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[W] Wenninger, 1974, has 119 figures: 1–5 for the Platonic solids, 6–18 for the Archimedean solids, 19–66 for stellated forms including the 4 regular nonconvex polyhedra, and ended with 67–119 for the nonconvex uniform polyhedra.
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Geometric variations with irregular faces can also be constructed. Some irregular pentahedra with six vertices may be called wedges . An irregular pentahedron can be a non- convex solid: Consider a non-convex (planar) quadrilateral (such as a dart ) as the base of the solid, and any point not in the base plane as the apex .
Alternatively, if you expand each of five cubes by moving the faces away from the origin the right amount and rotating each of the five 72° around so they are equidistant from each other, without changing the orientation or size of the faces, and patch the pentagonal and triangular holes in the result, you get a rhombicosidodecahedron ...
Vertex the (n−5)-face of the 5-polytope; Edge the (n−4)-face of the 5-polytope; Face the peak or (n−3)-face of the 5-polytope; Cell the ridge or (n−2)-face of the 5-polytope; Hypercell or Teron the facet or (n−1)-face of the 5-polytope
Two of them have pentagrammic {5/2} faces and two have pentagrammic vertex figures. These images show each form with a single face colored yellow to show the visible portion of that face. There are also an infinite number of regular star dihedra and hosohedra {2,p/q} and {p/q,2} for any star polygon {p/q}. While degenerate in Euclidean space ...
A Johnson solid is a convex polyhedron whose faces are all regular polygons. [1] Here, a polyhedron is said to be convex if the shortest path between any two of its vertices lies either within its interior or on its boundary, none of its faces are coplanar (meaning they do not share the same plane, and do not "lie flat"), and none of its edges are colinear (meaning they are not segments of the ...
It is an enneahedron (that is, a nine-sided polyhedron) [16] that can be realized with three non-adjacent square faces, and six more faces that are congruent irregular pentagons. [17] It is also known as an order-5 associahedron , a polyhedron whose vertices represent the 14 triangulations of a regular hexagon . [ 16 ]