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  2. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    Infinite number of uniform tilings in ... 15 for the Platonic ... ⁠ 5 / 3 ⁠ (3) ⁠ 5 / 2 ⁠ have some faces occurring as coplanar pairs. (Coxeter et al. 1954 ...

  3. List of polygons, polyhedra and polytopes - Wikipedia

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

    Vertex the (n−5)-face of the 5-polytope; Edge the (n−4)-face of the 5-polytope; Face the peak or (n−3)-face of the 5-polytope; Cell the ridge or (n−2)-face of the 5-polytope; Hypercell or Teron the facet or (n−1)-face of the 5-polytope

  4. Pentahedron - Wikipedia

    en.wikipedia.org/wiki/Pentahedron

    There is a third topological polyhedral figure with 5 faces, degenerate as a polyhedron: it exists as a spherical tiling of digon faces, called a pentagonal hosohedron with Schläfli symbol {2,5}. It has 2 ( antipodal point ) vertices, 5 edges, and 5 digonal faces.

  5. Platonic solid - Wikipedia

    en.wikipedia.org/wiki/Platonic_solid

    In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space.Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex.

  6. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    Edge, a 1-dimensional element; Face, a 2-dimensional element; Cell, a 3-dimensional element; Hypercell or Teron, a 4-dimensional element; Facet, an (n-1)-dimensional element; Ridge, an (n-2)-dimensional element; Peak, an (n-3)-dimensional element; For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and ...

  7. Triangular prism - Wikipedia

    en.wikipedia.org/wiki/Triangular_prism

    A triangular prism has 6 vertices, 9 edges, and 5 faces. Every prism has 2 congruent faces known as its bases, and the bases of a triangular prism are triangles. The triangle has 3 vertices, each of which pairs with another triangle's vertex, making up another 3 edges. These edges form 3 parallelograms as other faces. [2]

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  9. 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 ...

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