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Chamfered Octahedron


ChamferedOctahedron

A chamfered octahedron, which could also know known as a tritruncated rhombic dodecahedron, is a polyhedron obtained by chamfering a regular octahedron. The illustration above shows increasing amounts of chamfering applied to the regular octahedron.

ChamferedOctahedronEquilateral

An equilateral chamfered octahedron may be constructed by appropriate choice of the edge length ratio for chamfering. The unit equilateral chamfered octahedron has surface area and volume

S=8sqrt(2)+10sqrt(3)
(1)
V=1/3sqrt((2(1085+442sqrt(6)))/3)
(2)

and is implemented in Wolfram Language as PolyhedronData["EquilateralChamferedOctahedron"].


See also

Chamfered Polyhedron, Regular Octahedron

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References

Kuchel, P. "Al Rihla's Polyhedron: Truncated Rhombicdodecahedron Type 2." Aug. 23, 2022. https://community.wolfram.com/groups/-/m/t/2603714.McCooey, D. I. "Chamfered Octahedron." http://dmccooey.com/polyhedra/ChamferedOctahedron1.html.

Cite this as:

Weisstein, Eric W. "Chamfered Octahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChamferedOctahedron.html

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