A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive...

geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent...

Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two...

The regular icosahedron (or simply icosahedron) is a convex polyhedron that can be constructed from pentagonal antiprism by attaching two pentagonal pyramids...

This polyhedron can be used as the core for a set of stellations. A regular polyhedral compound can be defined as a compound which, like a regular polyhedron...

In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows...

In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-)  'many' and ἕδρον (-hedron)  'base, seat') is a three-dimensional figure...

convex polyhedron forms a 3-connected planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this...

10-demicube. Skew polygon Infinite skew polyhedron Abstract regular polytopes, p.7, p.17 Coxeter, Regular and Semi-Regular Polytopes II 2.34) Coxeter and Moser...

versa. For example, a traditional polytope is regular if all its facets and vertex figures are regular, but this is not necessarily so for an abstract...

In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges...

geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra. They may be obtained by stellating the regular convex dodecahedron and icosahedron...

cube or regular hexahedron is a three-dimensional solid object in geometry, which is bounded by six congruent square faces, a type of polyhedron. It has...

them is the regular icosahedron as its dual polyhedron. Other new polyhedrons can be constructed by using regular dodecahedron. The regular dodecahedron's...

truncation) of a regular polyhedron. Vertices are created mid-edge of the regular polyhedron and faces of the regular polyhedron and its dual are positioned...

A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex...

distances. The sum of the distances from any point in the interior of a regular polyhedron to the sides is independent of the location of the point. However...

In geometry, a quasiregular polyhedron is a uniform polyhedron that has exactly two kinds of regular faces, which alternate around each vertex. They are...

Wythoff symbol Tessellation Wallpaper group Regular polyhedron (the Platonic solids) Semiregular polyhedron (including the Archimedean solids) Hyperbolic...

for a regular polygon). A quasiregular polyhedron is a uniform polyhedron which has just two kinds of face alternating around each vertex. A regular polyhedron...

In abstract geometry, a hemicube is an abstract, regular polyhedron,[citation needed] produced by cutting a cube in half with a plane that passes through...

octahedron (pl.: octahedra or octahedrons) is a polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid composed of eight...

so a regular pentagram is {5/2}. A regular polyhedron having faces {n} with p faces joining around a vertex is denoted by {n, p}. The nine regular polyhedra...

is an abstract regular polyhedron, containing half the faces of a regular icosahedron. It can be realized as a projective polyhedron (a tessellation...

truncation operator applied to a regular polyhedron (or regular polytope) which creates a resulting uniform polyhedron (uniform polytope) with equal edge...

In geometry, a composite polyhedron is a convex polyhedron that produces other polyhedrons when sliced by a plane. Examples can be found in Johnson solids...

semiregular polyhedron (or semiregular polytope) is used variously by different authors. In its original definition, it is a polyhedron with regular polygonal...

In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality. There are two general...

abstract regular polyhedron, containing half the faces of a regular octahedron. It has 4 triangular faces, 6 edges, and 3 vertices. Its dual polyhedron is the...

cannot be a regular polyhedron, because there is no regular polygon that can form a regular tridecahedron, and there are only five known regular convex polyhedra...