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Cuboctahedron-Rhombic Dodecahedron Compound


CuboctahedronRhombDod
CuboctahedronRhombDodSolid

The polyhedron compound consisting of the cuboctahedron and its dual, the rhombic dodecahedron, illustrated in the left figure above. The right figure shows the solid common to the two polyhedra. If the cuboctahedron has unit edge length, the compound can be constructed by midpoint augmentation with heights

h_3=1/4sqrt(6)
(1)
h_4=1/2sqrt(2).
(2)

The resulting compound has side lengths

s_1=1/8sqrt(6)
(3)
s_2=1/2
(4)
s_3=1/4sqrt(6)
(5)
s_4=1/2sqrt(2),
(6)

and surface area and volume

S=3/4(4+5sqrt(2)+2sqrt(3))
(7)
V=(31)/(16)sqrt(2).
(8)

See also

Cuboctahedron, Dual Polyhedron, Polyhedron Compound, Rhombic Dodecahedron

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Cite this as:

Weisstein, Eric W. "Cuboctahedron-Rhombic Dodecahedron Compound." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cuboctahedron-RhombicDodecahedronCompound.html

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