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It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry. Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms have either regular star polygon faces or vertex figures or both. This list includes these:
A polytope is a geometric object with flat sides, which exists 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 specific examples.
Number of vertices V, edges E, Faces F and number of faces by type. Euler characteristic χ = V - E + F The vertex figures are on the left, followed by the Point groups in three dimensions#The seven remaining point groups , either tetrahedral T d , octahedral O h or icosahedral I h .
The numbers that can be used for the sides of a non-dihedral acute or obtuse Schwarz triangle that does not necessarily lead to only degenerate uniform polyhedra are 2, 3, 3/2, 4, 4/3, 5, 5/2, 5/3, and 5/4 (but numbers with numerator 4 and those with numerator 5 may not occur together). (4/2 can also be used, but only leads to degenerate ...
This is an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger. The book was written as a guide book to building polyhedra as physical models. It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes.
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.
Polyhedron: Class Number and properties ... This List of uniform polyhedra by spherical triangle groups them by the ... order 120 2 3 | 5 - 3.10.10 W10, U26, K31, C29 ...
List of uniform polyhedra by Wythoff symbol. ... Polyhedron: Class Number and properties ... order 120 2 3 | 5 - 3.10.10 W10, U26, K31, C29 Truncated great ...