大斜方十二面體

若大斜方十二面體的邊長為單位長，則其外接球半徑為：[14][6]

${\displaystyle R={\frac {\sqrt {11-4{\sqrt {5}}}}{2}}\approx 0.71689052337}$

大斜方十二面體共有兩種二面角，皆為正方形和十角星的二面角，但位置不同，一種位於五角星孔洞內，另一種位於三角形孔洞內。[8]

其中，位於五角星孔洞內的正方形和十角星的二面角角度約為58.28度：[6]

${\displaystyle \arccos \left({\frac {\sqrt {10\left(5-{\sqrt {5}}\right)}}{10}}\right)\approx 1.01722196789785\approx 58.282525589^{\circ }}$

位於三角形孔洞內的正方形和十角星的二面角角度約為31.717度：[6]

${\displaystyle \arccos \left({\frac {\sqrt {10\left(5+{\sqrt {5}}\right)}}{10}}\right)\approx 0.553574358897\approx 31.717474411^{\circ }}$

若大斜方十二面體邊長為單位長，且幾何中心位於原點，則其頂點座標為：[15]

${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}}\right)}$

${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {1}{2}}\right)}$

${\displaystyle \left(\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$

${\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,0,\,\pm {\frac {5-{\sqrt {5}}}{4}}\right)}$

${\displaystyle \left(0,\,\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}}\right)}$

${\displaystyle \left(\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,0\right)}$

${\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{2}}\right)}$

${\displaystyle (\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{4}})}$

${\displaystyle (\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}})}$