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Longer titles found: Semiregular polyhedron (view), Quasiregular polyhedron (view)

searching for Regular polyhedron 25 found (94 total)

Johnson solid (1,799 words) [view diff] no match in snippet view article find links to article

In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons. They are sometimes

Hemi-icosahedron (235 words) [view diff] exact match in snippet view article find links to article

In geometry, a hemi-icosahedron is an abstract regular polyhedron, containing half the faces of a regular icosahedron. It can be realized as a projective

Gravitation (M. C. Escher) (137 words) [view diff] exact match in snippet view article

and then coloured by hand in watercolour. It depicts a nonconvex regular polyhedron known as the small stellated dodecahedron. Each facet of the figure

Hemi-octahedron (159 words) [view diff] exact match in snippet view article find links to article

In geometry, a hemi-octahedron is an abstract regular polyhedron, containing half the faces of a regular octahedron. It has 4 triangular faces, 6 edges

Compound of five octahedra (369 words) [view diff] exact match in snippet view article find links to article

The compound of five octahedra is one of the five regular polyhedron compounds, and can also be seen as a stellation. It was first described by Edmund

Steinitz's theorem (5,973 words) [view diff] no match in snippet view article find links to article

In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices

Tetrahemihexahedron (909 words) [view diff] exact match in snippet view article find links to article

some of the faces form a group with half as many members as some regular polyhedron—here, three square faces form a group with half as many faces as the

Tutte graph (697 words) [view diff] exact match in snippet view article find links to article

Therefore, it is a counterexample to Tait's conjecture that every 3-regular polyhedron has a Hamiltonian cycle. Published by Tutte in 1946, it is the first

Exsphere (polyhedra) (722 words) [view diff] exact match in snippet view article

In geometry, the exsphere of a face of a regular polyhedron is the sphere outside the polyhedron which touches the face and the planes defined by extending

Walther graph (241 words) [view diff] exact match in snippet view article find links to article

the first known counterexample to Tait's conjecture that every 3-regular polyhedron has a Hamiltonian cycle. The Walther graph is an identity graph; its

List of uniform polyhedra by vertex figure (806 words) [view diff] exact match in snippet view article find links to article

Some are obtained by truncating the vertices of the regular or quasi-regular polyhedron. Others share the same vertices and edges as other polyhedron. The

20 (number) (632 words) [view diff] exact match in snippet view article

dodecahedron, on the other hand, has twenty vertices, likewise the most a regular polyhedron can have. This is because the icosahedron and dodecahdron are duals

Aperiodic set of prototiles (1,068 words) [view diff] exact match in snippet view article find links to article

have sharp corner turns at the vertices. Although a cube is the only regular polyhedron that admits of tessellation, many non-regular 3-dimensional shapes

Stellated octahedron (1,190 words) [view diff] exact match in snippet view article find links to article

symmetry is an octahedral symmetry. The stellated octahedron is also a regular polyhedron compound, when constructed as the union of two regular tetrahedra

Octacube (sculpture) (1,871 words) [view diff] exact match in snippet view article

analog of the octahedron is the 16-celled hexadecachoron. There is no regular polyhedron (Platonic solid) whose 4-D analog is the octacube (24-cell), but the

Triangle group (1,771 words) [view diff] exact match in snippet view article find links to article

together at two vertices. The spherical tiling corresponding to a regular polyhedron is obtained by forming the barycentric subdivision of the polyhedron

Nauru graph (1,378 words) [view diff] exact match in snippet view article find links to article

half-turns The Nauru graph has two different embeddings as a generalized regular polyhedron: a topological surface partitioned into edges, vertices, and faces

Abdulla A'zamov (1,124 words) [view diff] exact match in snippet view article find links to article

Aʼzamov (2019). The pursuit-evasion game on the 1-skeleton graph of the regular polyhedron. Abdulla Aʼzamov (2019). On the Сhernous’ko time-optimal problem for

Geodesic polyhedron (1,147 words) [view diff] exact match in snippet view article find links to article

in the form {3,q+}b,c, where {3,q} is the Schläfli symbol for the regular polyhedron with triangular faces, and q-valence vertices. The + symbol indicates

Chamfer (geometry) (1,299 words) [view diff] exact match in snippet view article

current one. The chamfer operator transforms GP(m,n) to GP(2m,2n). A regular polyhedron, GP(1,0), creates a Goldberg polyhedra sequence: GP(1,0), GP(2,0)

Eberhard's theorem (1,380 words) [view diff] exact match in snippet view article find links to article

is possible to choose a number of quadrilaterals that allows a 4-regular polyhedron to be realized. A strengthened version of Eberhard's theorem states

Sundial (14,026 words) [view diff] exact match in snippet view article find links to article

of multiple dial has sundials on every face of a Platonic solid (regular polyhedron), usually a cube. Extremely ornate sundials can be composed in this

Ideal polyhedron (3,229 words) [view diff] exact match in snippet view article find links to article

Dillencourt, Michael B.; Eppstein, David (2003), "Uninscribable 4-regular polyhedron", Electronic Geometry Models, Model No. 2003.08.001 Dillencourt, Michael

Mathematics and art (12,015 words) [view diff] exact match in snippet view article find links to article

here representing the divine perspective with a four-dimensional regular polyhedron. The painting shows the figure of Christ in front of the tessaract;

List of regular polytope compounds (1,947 words) [view diff] exact match in snippet view article find links to article

of antiprisms, for instance: A regular polyhedron compound can be defined as a compound which, like a regular polyhedron, is vertex-transitive, edge-transitive