List of small polyhedra by vertex count information
In geometry, a polyhedron is a solid in three dimensions with flat faces and straight edges. Every edge has exactly two faces, and every vertex is surrounded by alternating faces and edges. The smallest polyhedron is the tetrahedron with 4 triangular faces, 6 edges, and 4 vertices. Named polyhedra primarily come from the families of platonic solids, Archimedean solids, Catalan solids, and Johnson solids, as well as dihedral symmetry families including the pyramids, bipyramids, prisms, antiprisms, and trapezohedrons.
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faces or vertex figures or both. This list includes these: all 75 nonprismatic uniform polyhedra; a few representatives of the infinite sets of prisms and...
Extension of a polyhedron Goldberg polyhedron Listof books about polyhedraListof convex regular-faced polyhedraListofsmallpolyhedrabyvertexcount Near-miss...
set of regular hyperbolic tilings. The five convex regular polyhedra are called the Platonic solids. The vertex figure is given with each vertexcount. All...
For uniform polyhedra there is only one vertex type and therefore the vertex configuration fully defines the polyhedron. (Chiral polyhedra exist in mirror-image...
Wythoff symbol to vertex configuration fails for the exceptional five polyhedralisted above whose densities do not match the densities of their generating...
not generally counted as an Archimedean solid because it is not vertex-transitive. An even larger class than the convex uniform polyhedra is the Johnson...
star dodecahedra. They form three of the four Kepler–Poinsot polyhedra. They are the small stellated dodecahedron {5/2, 5}, the great dodecahedron {5,...
like a regular polyhedron, is vertex-transitive, edge-transitive, and face-transitive. Unlike the case ofpolyhedra, this is not equivalent to the symmetry...
the uniform polyhedra are listed below by their symmetry groups and subgrouped by their vertex arrangements. Regular polyhedra are labeled by their Schläfli...
coordination numbers of the vertices. In general, closo structures with n vertices are n-vertexpolyhedra. To predict the structure of a nido cluster, the...
is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent. Uniform polyhedra may...
a skew vertex figure, the three were not only the only skew apeirohedra in 3-dimensional Euclidean space, but they were the only skew polyhedra in 3-space...
cantellated polyhedra, which have similar Wythoff symbols. The vertex configuration is p/q.2r.p/(p − q).2r. The 2r-gon faces pass through the center of the model:...
In geometry, a uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets. The uniform polytopes in two dimensions...
the 1, 2, and 3 faces to share a vertex. The faces of a die may be placed clockwise or counterclockwise about this vertex. If the 1, 2, and 3 faces run counterclockwise...
tilings (or nine if the mirror-image pair of tilings counts as two). These can be described by their vertex configuration; for example, a semi-regular...
twenty-five uniform polyhedra that generate four-dimensional uniform polychora, they are the five Platonic solids, fifteen Archimedean solids counting two enantiomorphic...
Archimedean solid that is one of two quasiregular polyhedra, has eight triangles and six squares as faces. Inside, its vertex arrangement can be interpreted...
dodecahedron that is regular, which is composed of 12 regular pentagonal faces, three meeting at each vertex. It is one of the five Platonic solids. It has 12 faces...
of the great icosidodecahedron, as well as the Petrie polygon of two regular Kepler–Poinsot polyhedra. In total, ten non-prismatic uniform polyhedra contain...
finite cells and vertex figures (finite subgroups), and the second includes affine subgroups. The nine compact Coxeter groups are listed here with their...
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