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  2. 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.

  3. 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

  4. List of uniform polyhedra by vertex figure - Wikipedia

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

    For example, the cube has vertex figure 4.4.4, which is to say, three adjacent square faces. The possible faces are 3 - equilateral triangle; 4 - square; 5 - regular pentagon; 6 - regular hexagon; 8 - regular octagon; 10 - regular decagon; 5/2 - pentagram; 8/3 - octagram; 10/3 - decagram; Some faces will appear with reverse orientation which is ...

  5. List of polygons - Wikipedia

    en.wikipedia.org/wiki/List_of_polygons

    A pentagon is a five-sided polygon. A regular pentagon has 5 equal edges and 5 equal angles. In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain.

  6. 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+4 √ 5 / 2 ⁠ ≈ 2.233.

  7. Octahedron - Wikipedia

    en.wikipedia.org/wiki/Octahedron

    If this diagonal is oriented vertically with a height of 1, then the first five slices above occur at heights r, ⁠ 3 / 8 ⁠, ⁠ 1 / 2 ⁠, ⁠ 5 / 8 ⁠, and s, where r is any number in the range 0 < r ≤ ⁠ 1 / 4 ⁠, and s is any number in the range ⁠ 3 / 4 ⁠ ≤ s < 1.

  8. List of small polyhedra by vertex count - Wikipedia

    en.wikipedia.org/wiki/List_of_small_polyhedra_by...

    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.

  9. Face (geometry) - Wikipedia

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

    where V is the number of vertices, E is the number of edges, and F is the number of faces. This equation is known as Euler's polyhedron formula. Thus the number of faces is 2 more than the excess of the number of edges over the number of vertices. For example, a cube has 12 edges and 8 vertices, and hence 6 faces.