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...

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

A dual uniform polyhedron is the dual of a uniform polyhedron. Where a uniform polyhedron is vertex-transitive, a dual uniform polyhedron is face-transitive...

polyhedra: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron. The dual polyhedron of a cube is the regular octahedron...

Goldberg polyhedron is a dual polyhedron of a geodesic polyhedron. A consequence of Euler's polyhedron formula is that a Goldberg polyhedron always has...

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...

solids are the dual polyhedron of Archimedean solids, a set of thirteen polyhedrons with highly symmetric forms semiregular polyhedrons in which two or...

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

convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. As a Catalan solid, it is the dual polyhedron of the cuboctahedron...

polyhedron, i.e., an Archimedean solid that is not only vertex-transitive but also edge-transitive. It is radially equilateral. Its dual polyhedron is...

bipyramid as its dual polyhedron, many other polyhedrons are related to the triangular prism. A Johnson solid is a convex polyhedron with regular faces...

Buckminster Fuller. Its dual polyhedron is the tetrakis hexahedron. If the original truncated octahedron has unit edge length, its dual tetrakis hexahedron...

n-trapezohedron, n-antidipyramid, n-antibipyramid, or n-deltohedron, is the dual polyhedron of an n-gonal antiprism. The 2n faces of an n-trapezohedron are congruent...

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

vertex figure is denoted as 3 ⋅ 6 2 {\displaystyle 3\cdot 6^{2}} . Its dual polyhedron is triakis tetrahedron, a Catalan solid, shares the same symmetry as...

dimensions. A dual compound is composed of a polyhedron and its dual, arranged reciprocally about a common midsphere, such that the edge of one polyhedron intersects...

self-dual. The dual polyhedron of any of these polyhedra may be formed as the convex hull of the center points of each face of the primal polyhedron, so...

is a 4- or 5-vertex cycle. The dual polyhedron of the triaugmented triangular prism is an associahedron, a polyhedron with four quadrilateral faces and...

last names mean a polyhedron with 16 triangular faces. It is an example of deltahedron, and of a Johnson solid. The dual polyhedron of the gyroelongated...

dirhombidodecahedron, also called Skilling's figure, is a degenerate uniform star polyhedron. It was proven in 1970 that there are only 75 uniform polyhedra other...

thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. It is a Catalan solid, and the dual polyhedron...

derived from different approaches and the triangular prism as its dual polyhedron. Applications of a triangular bipyramid include trigonal bipyramidal...

truncated dodecahedron can be applied in the polyhedron's construction known as the augmentation. Examples of polyhedrons are the Johnson solids, whose constructions...

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...

20 triangular faces, with 5 faces meeting around each vertex. Its dual polyhedron is the regular dodecahedron {5, 3} having three regular pentagonal...

The shown dual polyhedra are dual to the canonical versions. The chamfered tetrahedron or alternate truncated cube is a convex polyhedron constructed:...

popular spherical polyhedron is the beach ball, thought of as a hosohedron. Some "improper" polyhedra, such as hosohedra and their duals, dihedra, exist...

Platonic solids and can be represented by its Schläfli symbol {5, 3}. The dual polyhedron is the regular icosahedron {3, 5}, having five equilateral triangles...

polyhedron with 12 vertices and 20 triangular faces. The dual polyhedron of a pentagonal bipyramid is the pentagonal prism. More generally, the dual polyhedron...

non-convex polyhedron is also a non-convex polyhedron. (By contraposition.) The dual of an isotoxal polyhedron is also an isotoxal polyhedron. (See the Dual polyhedron...