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...

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

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...

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...

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

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

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

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...

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...

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

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

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...

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

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...

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...

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...

Platonic solids, one of them is the regular icosahedron as its dual polyhedron. Other new polyhedrons can be constructed by using regular dodecahedron. The regular...

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

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...

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...

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...

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

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...

other Platonic solids, one of them is the regular dodecahedron as its dual polyhedron and has the historical background on the comparison mensuration. It...

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...

classified in parallel with their dual (uniform) polyhedron. The dual of a regular polyhedron is regular, while the dual of an Archimedean solid is a Catalan...

geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4. It has 7 faces (4 triangles and 3 squares), 12 edges,...