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Chamfered Tetrahedron


ChamferedTetrahedron

A chamfered tertrahedron, also known as the alternate truncated cube, is a polyhedron obtained by chamfering a regular tetrahedron. The illustration above shows increasing amounts of chamfering applied to the regular tetrahedron.

It is a (non-regular) decahedron.

ChamferedTetrahedronEquilateral

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

S=6+6sqrt(2)+sqrt(3)
(1)
V=5/2+(19)/(6sqrt(2))
(2)

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


See also

Chamfered Polyhedron, Regular Tetrahedron

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References

McCooey, D. I. "Chamfered Tetrahedron." http://dmccooey.com/polyhedra/ChamferedTetrahedron1.html.

Cite this as:

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

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