the uniform polyhedra. This List of uniform polyhedra by spherical triangle groups them by the Wythoff symbol. The vertex figure can be discovered by considering...

the uniform polyhedra. The Wythoff construction is able to construct almost all of the uniform polyhedra from the acute and obtuse Schwarz triangles. The...

Schwarz triangles. All the uniform polyhedra are listed below by their symmetry groups and subgrouped by their vertex arrangements. Regular polyhedra are...

so many of the uniform polyhedra are also star polyhedra. There are two infinite classes of uniform polyhedra, together with 75 other polyhedra. They are...

"3D convex uniform polyhedra x3x5o - ti". Editable printable net of a truncated icosahedron with interactive 3D view The Uniform Polyhedra "Virtual Reality...

topological polyhedra (even with all faces triangles) that cannot be realized as acoptic polyhedra. One modern approach is based on the theory of abstract...

vertex count. All these polyhedra have an Euler characteristic (χ) of 2. In spherical geometry, regular spherical polyhedra (tilings of the sphere) exist that...

Dodecahedron Icosahedron hosohedron dihedron Henagon#In spherical geometry Kepler–Poinsot polyhedra Small stellated dodecahedron Great dodecahedron Great...

they are two of the thirteen Catalan solids. The uniform polyhedra form a much broader class of polyhedra. These figures are vertex-uniform and have one...

geometry, a uniform 4-polytope (or uniform polychoron) is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces...

tilings Uniform tilings in hyperbolic plane List of uniform polyhedra List of uniform polyhedra by Schwarz triangle Coxeter Regular Polytopes, Third edition...

compound List of uniform polyhedra List of uniform polyhedra by Schwarz triangle Coxeter, H.S.M., M. S. Longuet-Higgins and J.C.P Miller, Uniform Polyhedra, Phil...

Analysis of the Five Platonic Solids and Other Semi-Regular Polyhedra The Uniform Polyhedra Virtual Reality Polyhedra – The Encyclopedia of Polyhedra Conway...

right triangles (p q 2), there are two regular tilings, represented by Schläfli symbol {p,q} and {q,p}. There are an infinite number of uniform tilings...

tiling. There are 9 distinct uniform colorings of a triangular tiling. (Naming the colors by indices on the 6 triangles around a vertex: 111111, 111112...

hyperbolic plane. Uniform tilings are related to the finite uniform polyhedra; these can be considered uniform tilings of the sphere. Most uniform tilings can...

in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some...

There are many relations among the uniform polyhedra. Some are obtained by truncating the vertices of the regular or quasi-regular polyhedron. Others share...

side faces. Uniform antiprisms form an infinite class of vertex-transitive polyhedra, as do uniform prisms. For n = 2, we have the digonal antiprism (degenerate...

Retrieved on 2008-01-31. Satterly, John (1958). "The Moments of Inertia of Some Polyhedra". The Mathematical Gazette. 42 (339). Mathematical Association:...

Richard. "3D convex uniform polyhedra x3o5o – ike". Hartley, Michael. "Dr Mike's Math Games for Kids". K.J.M. MacLean, A Geometric Analysis of the Five Platonic...

identically to spherical polyhedra. An illustration of the formula on all Platonic polyhedra is given below. The surfaces of nonconvex polyhedra can have various...

of antiprisms. The uniform star polyhedra include a further 4 regular star polyhedra, the Kepler-Poinsot polyhedra, and 53 semiregular star polyhedra...

composed of four triangular faces, six straight edges, and four vertices. The tetrahedron is the simplest of all the ordinary convex polyhedra. The tetrahedron...

tetrahedron Platonic solid Archimedean solid Kepler-Poinsot polyhedra Johnson solid Uniform polyhedron Polyhedral compound Hilbert's third problem Deltahedron...

enumerated by Archimedes. They belong to the class of convex uniform polyhedra, the convex polyhedra with regular faces and symmetric vertices, which is...

the sequence are omnitruncated polyhedra (zonohedra), shown below as spherical tilings. For p > 6, they are tilings of the hyperbolic plane, starting...

circles from projections of two other polyhedra, form the 31 great circles of the spherical icosahedron used in construction of geodesic domes. It has four...

we list the seventy-five nondihedral uniform polyhedra, as well as the five pentagonal prisms and antiprisms, grouped by generating Schwarz triangles."...

octagonal faces. All isotoxal polyhedra listed above can be made as isotoxal tilings of the sphere. In addition as spherical tilings, there are two other...