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  2. Dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Dodecahedron

    The concave equilateral dodecahedron, called an endo-dodecahedron. [clarification needed] A cube can be divided into a pyritohedron by bisecting all the edges, and faces in alternate directions. A regular dodecahedron is an intermediate case with equal edge lengths. A rhombic dodecahedron is a degenerate case with the 6 crossedges reduced to ...

  3. Rhombicosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombicosidodecahedron

    In geometry, the Rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges.

  4. Regular dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Regular_dodecahedron

    The regular dodecahedron can be found in many popular cultures: Roman dodecahedron, the children's story, toys, and painting arts. It can also be found in nature and supramolecules, as well as the shape of the universe. The skeleton of a regular dodecahedron can be represented as the graph called the dodecahedral graph, a Platonic graph.

  5. Snub (geometry) - Wikipedia

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

    In geometry, a snub is an operation applied to a polyhedron. The term originates from Kepler 's names of two Archimedean solids , for the snub cube ( cubus simus ) and snub dodecahedron ( dodecaedron simum ).

  6. Elongated dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Elongated_dodecahedron

    In geometry, the elongated dodecahedron, [1] extended rhombic dodecahedron, rhombo-hexagonal dodecahedron [2] or hexarhombic dodecahedron [3] is a convex dodecahedron with 8 rhombic and 4 hexagonal faces. The hexagons can be made equilateral, or regular depending on the shape of the rhombi.

  7. 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. There are only five such polyhedra:

  8. Rhombus - Wikipedia

    en.wikipedia.org/wiki/Rhombus

    The rhombic dodecahedron is a convex polyhedron with 12 congruent rhombi as its faces. The rhombic triacontahedron is a convex polyhedron with 30 golden rhombi (rhombi whose diagonals are in the golden ratio) as its faces. The great rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron with 30 intersecting rhombic faces.

  9. Schläfli symbol - Wikipedia

    en.wikipedia.org/wiki/Schläfli_symbol

    The dodecahedron is a regular polyhedron with Schläfli symbol {5,3}, having 3 pentagons around each vertex.. In geometry, the Schläfli symbol is a notation of the form {,,,...} that defines regular polytopes and tessellations.