## Radius of Gyration (Rg) of the 13 Archimedean Solids

The values for the Volume (V), the Surface (S), the out-sphere (circum-sphere) radius (ro), the mid-sphere radius (rm), the Radius of Gyration (Rg) and the moment of inertia (I) of the 13 Archimedean Solids with edge length a = 1 and mass m = 1 are compiled in the following table.

 Solid Volume Surface ro rm Rg I (m*a^2) Truncated Tetrahedron 2.71058 12.12436 1.17260 1.06066 0.72005 0.34565 Truncated Octahedron 11.31371 26.78461 1.58114 1.50000 1.08972 0.79167 Truncated Cube 13.59966 32.43466 1.77882 1.70711 1.18122 0.93018 Truncated Icosahedron 55.28773 72.60725 2.47802 2.42705 1.83258 2.23891 Truncated Dodecahedron 85.03966 100.99076 2.96945 2.92705 2.12672 3.01529 Cuboctahedron 2.35702 9.46410 1.00000 0.86603 0.64807 0.28000 Icosidodecahedron 13.83553 29.30598 1.61803 1.53884 1.15787 0.89378 Snub Cube 7.88948 19.85641 1.34371 1.24722 0.95857 0.61257 Snub Dodecahedron 37.61665 55.28674 2.15584 2.09705 1.61125 1.73077 Small Rhombicuboctahedron 8.71405 21.46410 1.39897 1.30656 0.99132 0.65514 Great Rhombicuboctahedron 41.79899 61.75517 2.31761 2.26303 1.67650 1.87377 Small Rhombicosidodecahedron 41.61532 59.30598 2.23295 2.17625 1.66620 1.85081 Great Rhombicosidodecahedron 206.80340 174.29203 3.80239 3.76938 2.84666 5.4023

Table 1. Shape parameters and calculated values for Rg (rounded) for the 13 Archimedean solids with edge length = 1. Units are arbitrary.

Author: M.Kriechbaum, TU-Graz (2013), e-mail: manfred.kriechbaum@tugraz.at