TOPICS
Search

Truncated Dodecahedron-Triakis Icosahedron Compound


TruncatedDodecDualCompound

The polyhedron compound of the truncated dodecahedron and its dual, the triakis icosahedron. The compound can be constructed from a truncated dodecahedron of unit edge length by midpoint augmentation with heights

h_3=1/(372)sqrt(3)(1+5sqrt(5))
(1)
h_(10)=1/2sqrt(1/2(5+sqrt(5))).
(2)

The resulting solid has edge lengths

s_1=1/(62)sqrt(5/6(397+sqrt(5)))
(3)
s_2=1/2
(4)
s_3=1/2sqrt(1/2(5+sqrt(5)))
(5)
s_4=1/4(5+sqrt(5)),
(6)

circumradius

 R=1/2sqrt(1/2(37+15sqrt(5))),
(7)

surface area given by a root of a 32nd order polynomial with large integer coefficients, and volume

 V=5/(1488)(15997+7693sqrt(5)).
(8)

See also

Polyhedron Compound, Triakis Icosahedron, Truncated Dodecahedron, Truncation

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Truncated Dodecahedron-Triakis Icosahedron Compound." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TruncatedDodecahedron-TriakisIcosahedronCompound.html

Subject classifications