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  2. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    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:

  3. List of uniform polyhedra by vertex figure - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra...

    Numbering systems: W - number used by Wenninger in polyhedra models, U - uniform indexing, K - Kaleido indexing, C - numbering used in Coxeter et al. 'Uniform Polyhedra'. Number of vertices V, edges E, Faces F and number of faces by type. Euler characteristic χ = V - E + F

  4. List of polygons, polyhedra and polytopes - Wikipedia

    en.wikipedia.org/wiki/List_of_polygons...

    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.

  5. List of uniform polyhedra by Wythoff symbol - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra...

    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 ...

  6. Regular polyhedron - Wikipedia

    en.wikipedia.org/wiki/Regular_polyhedron

    A regular polyhedron is identified by its Schläfli symbol of the form {n, m}, where n is the number of sides of each face and m the number of faces meeting at each vertex. There are 5 finite convex regular polyhedra (the Platonic solids), and four regular star polyhedra (the Kepler–Poinsot polyhedra), making nine regular polyhedra in all. In ...

  7. List of uniform polyhedra by spherical triangle - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra...

    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 ...

  8. List of Wenninger polyhedron models - Wikipedia

    en.wikipedia.org/wiki/List_of_Wenninger...

    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.

  9. List of uniform polyhedra by Schwarz triangle - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra...

    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 ...

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