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  2. Rhombic dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombic_dodecahedron

    The rhombic dodecahedron can be seen as a degenerate limiting case of a pyritohedron, with permutation of coordinates (±1, ±1, ±1) and (0, 1 + h, 1 − h 2) with parameter h = 1. These coordinates illustrate that a rhombic dodecahedron can be seen as a cube with six square pyramids attached to each face, allowing them to fit together into a ...

  3. Rhombicosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombicosidodecahedron

    Net 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. 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 ...

  5. First stellation of the rhombic dodecahedron - Wikipedia

    en.wikipedia.org/wiki/First_stellation_of_the...

    In geometry, the first stellation of the rhombic dodecahedron is a self-intersecting polyhedron with 12 faces, each of which is a non-convex hexagon. It is a stellation of the rhombic dodecahedron and has the same outer shell and the same visual appearance as two other shapes: a solid, Escher's solid, with 48 triangular faces, and a polyhedral compound of three flattened octahedra with 24 ...

  6. File:Rhombicdodecahedron net.svg - Wikipedia

    en.wikipedia.org/wiki/File:Rhombicdodecahedron...

    Date/Time Thumbnail Dimensions User Comment; current: 23:21, 22 December 2011: 520 × 640 (1 KB): OgreBot (BOT): Reverting to most recent version before archival

  7. Table of polyhedron dihedral angles - Wikipedia

    en.wikipedia.org/wiki/Table_of_polyhedron...

    Rhombic hexahedron (Dual of tetratetrahedron) — V(3.3.3.3) arccos (0) = ⁠ π / 2 ⁠ 90° Rhombic dodecahedron (Dual of cuboctahedron) — V(3.4.3.4) arccos (-⁠ 1 / 2 ⁠) = ⁠ 2 π / 3 ⁠ 120° Rhombic triacontahedron (Dual of icosidodecahedron) — V(3.5.3.5) arccos (-⁠ √ 5 +1 / 4 ⁠) = ⁠ 4 π / 5 ⁠ 144° Medial rhombic ...

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  9. Catalan solid - Wikipedia

    en.wikipedia.org/wiki/Catalan_solid

    Additionally, two Catalan solids, the rhombic dodecahedron and rhombic triacontahedron, are edge-transitive, meaning their edges are symmetric to each other. [citation needed] Some Catalan solids were discovered by Johannes Kepler during his study of zonohedra, and Eugene Catalan completed the list of the thirteen solids in 1865. [4]