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Tetragonal Trapezohedron


Trapezohedron04

The tetragonal trapezohedron is the dual of the square antiprism. For a square antiprism with unit edge lengths, the edge lengths of the corresponding tetragonal trapezohedron are

s_1=sqrt(sqrt(2)-1)
(1)
s_2=sqrt(1/2+1/(sqrt(2))),
(2)

and the corresponding surface area and volume are

S=2sqrt(2+4sqrt(2))
(3)
V=1/3sqrt(4+3sqrt(2)).
(4)
TetragonalTrapezohedronSkeleton

The skeleton of the tetragonal trapezohedron is a non-cubic graph (it has degree sequence (3, 3, 3, 3, 3, 3, 3, 3, 4, 4)) in which all faces touch an even number of sides but the graph is not three-colorable.


See also

Square Antiprism, Trapezohedron

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Cite this as:

Weisstein, Eric W. "Tetragonal Trapezohedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TetragonalTrapezohedron.html

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