菱形三十面体
体積: V = 4 5 + 2 5 a 3 ≈ 12.3107 a 3 {\displaystyle V=4{\sqrt {5+2{\sqrt {5}}}}\,a^{3}\approx 12.3107a^{3}}
内接球の半径: r i = φ 2 1 + φ 2 a = 1 + 2 5 a ≈ 1.37638 a {\displaystyle r_{\mathrm {i} }={\frac {\varphi ^{2}}{\sqrt {1+\varphi ^{2}}}}\,a={\sqrt {1+{\frac {2}{\sqrt {5}}}}}\,a\approx 1.37638a}
辺の中点を通る球の半径: r m = ( 1 + 1 5 ) a ≈ 1.44721 a {\displaystyle r_{\mathrm {m} }=\left(1+{\frac {1}{\sqrt {5}}}\right)\,a\approx 1.44721a}