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: Infinite...

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...

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

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

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

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

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

four-dimensional polyhedra that cannot be combined with their duals to form five-dimensional antiprisms. Uniform star antiprisms are named by their star polygon...

is one of a family of uniform polyhedra related to the cube and regular octahedron. The cube is topologically related as a part of sequence of regular...

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...

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...

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...

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

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...

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

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...

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

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

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

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...

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...

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

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

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

convex uniform polyhedra o3o5x – doe". Editable printable net of a dodecahedron with interactive 3D view The Uniform Polyhedra Origami Polyhedra – Models...

faces pass through the center of the model: if represented as faces of spherical polyhedra, they cover an entire hemisphere and their edges and vertices lie...