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Cube 6-Compound


Cube6-CompoundC3Cube 6-compound paper sculpture

A number of cube 6-compounds can be constructed. The compound illustrated above is obtained by combining six cubes, each rotated by 1/6 of a turn about the line joining the centroids of opposite faces of an initial cube. The illustration at right above shows a paper sculpture of this compound.

Cube6-CompoundNetC3

A net for constructing the above compound is illustrated above, where

s_1=sqrt((79)/(784)-(13)/(98sqrt(2)))
(1)
s_2=1/2sqrt(215-152sqrt(2))
(2)
s_3=1/2(3sqrt(2)-4)
(3)
s_4=1/2sqrt(51-36sqrt(2))
(4)
s_5=1/2sqrt(51-36sqrt(2))
(5)
s_6=1/2sqrt(95-64sqrt(2))
(6)
s_7=1/4sqrt(255-180sqrt(2))
(7)
s_8=sqrt(9/8-3/(2sqrt(2)))
(8)
s_9=1/(14)sqrt(15)
(9)
s_(10)=sqrt(7/(16)-1/(2sqrt(2)))
(10)
s_(11)=1/2(2-sqrt(2))
(11)
s_(12)=1/7(3sqrt(2)-2)
(12)
s_(13)=1.
(13)

It has surface area

 S=171sqrt(2)-(1626)/7 approx 9.54,
(14)

compared to S=6 for each of the six constituent cubes.

Cube6-CompoundC4

The compound illustrated above is obtained by combining six cubes, each rotated by 1/8 of a turn about the line joining the centroids of opposite faces of an initial cube.


See also

Cube, Cube 2-Compound, Cube 3-Compound, Cube 4-Compound, Cube 5-Compound, Cube 7-Compound, Cube 10-Compound, Cube 20-Compound, Cube-Octahedron Compound, Polyhedron Compound

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References

Hart, G. "Cube Six-Compound." http://www.georgehart.com/virtual-polyhedra/vrml/cubes_S4_D2.wrl.Verheyen, H. F. Symmetry Orbits. Boston, MA: Birkhäuser, 2007.

Cite this as:

Weisstein, Eric W. "Cube 6-Compound." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cube6-Compound.html

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