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  2. Rhombic dodecahedral honeycomb - Wikipedia

    en.wikipedia.org/wiki/Rhombic_dodecahedral_honeycomb

    The vertices with the obtuse rhombic face angles have 4 cells. The vertices with the acute rhombic face angles have 6 cells. The rhombic dodecahedron can be twisted on one of its hexagonal cross-sections to form a trapezo-rhombic dodecahedron, which is the cell of a somewhat similar tessellation, the Voronoi diagram of hexagonal close-packing.

  3. 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 ...

  4. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet. Tessellations ... Truncated rhombic dodecahedron; Truncated ...

  5. Parallelohedron - Wikipedia

    en.wikipedia.org/wiki/Parallelohedron

    The rhombic dodecahedron, generated from four line segments, no two of which are parallel to a common plane. Its most symmetric form is generated by the four long diagonals of a cube. [2] It tiles space to form the rhombic dodecahedral honeycomb. The elongated dodecahedron, generated from five line segments, with two triples of coplanar segments.

  6. 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 ...

  7. Honeycomb (geometry) - Wikipedia

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

    Non-convex cells which pack without overlapping, analogous to tilings of concave polygons. These include a packing of the small stellated rhombic dodecahedron, as in the Yoshimoto Cube. Overlapping of cells whose positive and negative densities 'cancel out' to form a uniformly dense continuum, analogous to overlapping tilings of the plane.

  8. Truncated icosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Truncated_icosidodecahedron

    In geometry, a truncated icosidodecahedron, rhombitruncated icosidodecahedron, [1] great rhombicosidodecahedron, [2] [3] omnitruncated dodecahedron or omnitruncated icosahedron [4] is an Archimedean solid, one of thirteen convex, isogonal, non-prismatic solids constructed by two or more types of regular polygon faces.

  9. Synergetics (Fuller) - Wikipedia

    en.wikipedia.org/wiki/Synergetics_(Fuller)

    space-filler, 2As + 1B Tetrahedron 1 self dual, unit volume Coupler 1 space filling oblate octa Cuboctahedron 2.5 edges 1/2, vol. = 1/8 of 20 Duo-Tet Cube 3 24 MITEs Octahedron 4 dual of cube, spacefills w/ tet Rhombic Triacontahedron 5 radius = ~0.9994, vol. = 120 Ts Rhombic Triacontahedron 5+ radius = 1, vol. = 120 Es Rhombic Dodecahedron 6