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Great Rhombicosidodecahedron (Archimedean)


An Archimedean Solid also known as the Rhombitruncated Icosidodecahedron. It is sometimes improperly called the Truncated Icosidodecahedron, a name which is inappropriate since Truncation would yield Rectangular instead of Square. The great rhombicosidodecahedron is also Uniform Polyhedron $U_{28}$. Its Dual is the Disdyakis Triacontahedron, also called the Hexakis Icosahedron. It has Schläfli Symbol t $\left\{{3\atop 5}\right\}$ and Wythoff Symbol $2\,3\,5\,\vert$. The Inradius, Midradius, and Circumradius for $a=1$ are

$\displaystyle r$ $\textstyle =$ $\displaystyle {\textstyle{1\over 241}}(105+6\sqrt{5}\,)\sqrt{31+12\sqrt{5}}\approx 3.73665$  
$\displaystyle \rho$ $\textstyle =$ $\displaystyle {\textstyle{1\over 2}}\sqrt{30+12\sqrt{5}}\approx 3.76938$  
$\displaystyle R$ $\textstyle =$ $\displaystyle {\textstyle{1\over 2}}\sqrt{31+12\sqrt{5}}\approx 3.80239.$  

See also Small Rhombicosidodecahedron


Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 137, 1987.

© 1996-9 Eric W. Weisstein