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  2. Rhombic dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombic_dodecahedron

    In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. As a Catalan solid, it is the dual polyhedron of the cuboctahedron. As a parallelohedron, the rhombic dodecahedron can be used to tesselate its copies in space creating a rhombic dodecahedral honeycomb.

  3. 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.

  4. Synergetics (Fuller) - Wikipedia

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

    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 space-filler, dual to cuboctahedron Rhombic Triacontahedron 7.5 ...

  5. Honeycomb (geometry) - Wikipedia

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

    A necessary condition for a polyhedron to be a space-filling polyhedron is that its Dehn invariant must be zero, [3] [4] ruling out any of the Platonic solids other than the cube. Five space-filling convex polyhedra can tessellate 3-dimensional euclidean space using translations only.

  6. 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.

  7. Rhombicosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombicosidodecahedron

    [1] [2] There are different truncations of a rhombic triacontahedron into a topological rhombicosidodecahedron: Prominently its rectification (left), the one that creates the uniform solid (center), and the rectification of the dual icosidodecahedron (right), which is the core of the dual compound.

  8. Polytope compound - Wikipedia

    en.wikipedia.org/wiki/Polytope_compound

    A regular polyhedral compound can be defined as a compound which, like a regular polyhedron, is vertex-transitive, edge-transitive, and face-transitive.Unlike the case of polyhedra, this is not equivalent to the symmetry group acting transitively on its flags; the compound of two tetrahedra is the only regular compound with that property.

  9. Archimedean solid - Wikipedia

    en.wikipedia.org/wiki/Archimedean_solid

    3.4.4.4: 8 triangles 18 squares 48 24 O h: Truncated cuboctahedron: 4.6.8: 12 squares 8 hexagons 6 octagons 72 48 O h: Snub cube: 3.3.3.3.4: 32 triangles 6 squares 60 24 O Icosidodecahedron: 3.5.3.5: 20 triangles 12 pentagons: 60 30 I h: Truncated dodecahedron: 3.10.10: 20 triangles 12 decagons: 90 60 I h: Truncated icosahedron: 5.6.6: 12 ...