${\displaystyle {\sqrt {3))a^{2))$

${\displaystyle \approx 1.732a^{2))$

體積：${\displaystyle {1 \over 12}{\sqrt {2))a^{3))$${\displaystyle \approx 0.118a^{3))$
二面角角度：${\displaystyle \arccos {\frac {1}{3))}$${\displaystyle \approx 70^{\circ }52'}$
外接球半徑：${\displaystyle {\frac {\sqrt {6)){4))a}$${\displaystyle \approx 0.612a}$
內切球半徑：${\displaystyle {\frac {\sqrt {6)){12))a}$${\displaystyle \approx 0.204a}$
對偶多面體：正四面體

${\displaystyle 6a^{2}\ }$

體積：${\displaystyle a^{3}\ }$
二面角角度：${\displaystyle 90^{\circ ))$
外接球半徑：${\displaystyle {\sqrt {\frac {3}{4))}a}$${\displaystyle \approx 0.866a}$
內切球半徑：${\displaystyle {\frac {a}{2))}$
對偶多面體：正八面體

${\displaystyle 2{\sqrt {3))a^{2))$

${\displaystyle \approx 3.464a^{2))$

體積：${\displaystyle {\frac {\sqrt {2)){3))a^{3))$${\displaystyle \approx 0.471a^{3))$
二面角角度：${\displaystyle \arccos \left(-{\frac {1}{3))\right)}$${\displaystyle \approx 109^{\circ }28'}$
外接球半徑：${\displaystyle {\frac {a}{\sqrt {2))))$${\displaystyle \approx 0.707a}$
內切球半徑：${\displaystyle {\frac {a}{\sqrt {6))))$${\displaystyle \approx 0.408a}$
對偶多面體：立方體

${\displaystyle 3{\sqrt {25+10{\sqrt {5))))a^{2))$

${\displaystyle \approx 20.65a^{2))$

體積：${\displaystyle {1 \over 4}(15+7{\sqrt {5)))a^{3))$${\displaystyle \approx 7.663a^{3))$
二面角角度：${\displaystyle \arccos {\bigg (}{-{\frac {\sqrt {5)){5))}{\bigg )))$${\displaystyle \approx 116^{\circ }57'}$
外接球半徑：${\displaystyle {\frac {\sqrt {6)){4)){\sqrt {3+{\sqrt {5))))a}$${\displaystyle \approx 1.401a}$
內切球半徑：${\displaystyle {\frac {a}{4)){\sqrt {\frac {50+22{\sqrt {5))}{5))))$${\displaystyle \approx 1.114a}$
對偶多面體：正二十面體

${\displaystyle 5{\sqrt {3))a^{2))$

${\displaystyle \approx 8.660a^{2))$

體積：${\displaystyle {5 \over 12}(3+{\sqrt {5)))a^{3))$${\displaystyle \approx 2.182a^{3))$
二面角角度：${\displaystyle \arccos {\bigg (}{-{\frac {\sqrt {5)){3))}{\bigg )))$${\displaystyle \approx 138^{\circ }19'}$
外接球半徑：${\displaystyle {\frac {a}{4)){\sqrt {10+2{\sqrt {5))))}$${\displaystyle \approx 0.951a}$
內切球半徑：${\displaystyle {\frac {a}{12)){\sqrt {3))\left(3+{\sqrt {5))\right)}$${\displaystyle \approx 0.756a}$
對偶多面體：正十二面體