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  2. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    The 5 Platonic solids are called a tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron with 4, 6, 8, 12, and 20 sides respectively. The regular hexahedron is a cube . Table of polyhedra

  3. Rhombicosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombicosidodecahedron

    where φ = ⁠ 1 + √ 5 / 2 ⁠ is the golden ratio. Therefore, the circumradius of this rhombicosidodecahedron is the common distance of these points from the origin, namely √ φ 6 +2 = √ 8φ+7 for edge length 2. For unit edge length, R must be halved, giving R = ⁠ √ 8φ+7 / 2 ⁠ = ⁠ √ 11+45 / 2 ⁠ ≈ 2.233.

  4. 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

  5. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    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 a vertex is a peak.

  6. 5-polytope - Wikipedia

    en.wikipedia.org/wiki/5-polytope

    A 5-polytope is a closed five-dimensional figure with vertices, edges, faces, and cells, and 4-faces.A vertex is a point where five or more edges meet. An edge is a line segment where four or more faces meet, and a face is a polygon where three or more cells meet.

  7. Face (geometry) - Wikipedia

    en.wikipedia.org/wiki/Face_(geometry)

    [3] [5] [6] A face of dimension k is called a k-face. For example, the polygonal faces of an ordinary polyhedron are 2-faces. In set theory, the set of faces of a polytope includes the polytope itself and the empty set, where the empty set is for consistency given a "dimension" of −1. For any n-polytope (n-dimensional polytope), −1 ≤ k ≤ n.

  8. Polyhedron - Wikipedia

    en.wikipedia.org/wiki/Polyhedron

    It is possible for some polyhedra to change their overall shape, while keeping the shapes of their faces the same, by varying the angles of their edges. A polyhedron that can do this is called a flexible polyhedron. By Cauchy's rigidity theorem, flexible polyhedra must be non-convex. The volume of a flexible polyhedron must remain constant as ...

  9. Archimedean solid - Wikipedia

    en.wikipedia.org/wiki/Archimedean_solid

    Vertex configurations [4] Faces [5] Edges [5] Vertices [5] Point group [6] Truncated tetrahedron: 3.6.6: 4 triangles 4 hexagons: 18 12 T d: Cuboctahedron: 3.4.3.4: 8 triangles 6 squares: 24 12 O h: Truncated cube: 3.8.8: 8 triangles 6 octagons: 36 24 O h: Truncated octahedron: 4.6.6: 6 squares 8 hexagons 36 24 O h: Rhombicuboctahedron: 3.4.4.4 ...

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