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Small Rhombicuboctahedron-Deltoidal Icositetrahedron Compound

SmallRhombicDualCompound

The polyhedron compound of the small rhombicuboctahedron and its dual, the deltoidal icositetrahedron. The compound can be constructed from a small rhombicuboctahedron of unit edge length by midpoint augmentation with heights

h_3=1/(42)sqrt(3)(3-sqrt(2))
(1)
h_4=1/2(sqrt(2)-1).
(2)

The compound generated from a small rhombicuboctahedron of unit edge lengths has edge lengths

s_1=1/7sqrt(1/2(10-sqrt(2)))
(3)
s_2=1/2
(4)
s_3=sqrt(1/2(2-sqrt(2)))
(5)
s_4=1/2sqrt(2),
(6)

circumradius

R=sqrt(2),
(7)

surface area

S=3/(14)(42+sqrt(11770-6224sqrt(2)+14sqrt(34869-18672sqrt(2))))
(8)

and volume

V=1/(28)(71+135sqrt(2).
(9)

See also

Deltoidal Icositetrahedron, Polyhedron Compound, Small Rhombicuboctahedron

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Cite this as:

Weisstein, Eric W. "Small Rhombicuboctahedron-Deltoidal Icositetrahedron Compound." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SmallRhombicuboctahedron-DeltoidalIcositetrahedronCompound.html

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