Honey bees use the geometry of rhombic dodecahedra to form honeycombs from a tessellation of cells each of which is a hexagonal prism capped with half a rhombic dodecahedron.
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About a hundred of these dodecahedra have been found from Wales to Hungary and Spain and to the east of Italy, with most found in Germany and France.
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In 20th-century art, dodecahedra appear in the work of M . C . Escher, such as his lithographs " Gravitation " ( 1952 ).
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The unfolded cube can be stellated rhombic dodecahedra, each of which comprise half the volume of the original cube, making it a kind of three-dimensional dissection puzzle.
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There is another honeycomb in hyperbolic 3-space called the order-4 dodecahedral honeycomb, { 5, 3, 4 }, which has only four dodecahedra per edge.
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It can be constructed by creating two coinciding dodecahedra in 3-space, and translating each copy in opposite perpendicular directions in 4-space until their separation equals their edge length.
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This family has order 120 & times; 120 = 24 & times; 600 = 14400 : 120 for each of the 120 dodecahedra, or 24 for each of the 600 tetrahedra.
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These projections are also used in showing the four-dimensional 120-cell, a regular 4-dimensional polytope, constructed from 120 dodecahedra, projecting it down to 3-dimensions.
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The icosahedron, as a uniform " snub tetrahedron " 25px, is similar to these snub-pair compounds : compound of two snub cubes and compound of two snub dodecahedra.
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Although regular dodecahedra do not exist in crystals, the pyritohedron form occurs in the crystals of the mineral pyrite, and it may be an inspiration for the discovery of the regular Platonic solid form.
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