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