Compound of five truncated tetrahedra

<h2 id="cartesian-coordinates">Cartesian coordinates</h2>
<p><a href="/facts/Cartesian_coordinates/lkTqvMmB">Cartesian coordinates</a> for the vertices of this compound are all the cyclic permutations of
</p>
(±1, ±1, ±3)
(±τ−1, ±(−τ−2), ±2τ)
(±τ, ±(−2τ−1), ±τ2)
(±τ2, ±(−τ−2), ±2)
(±(2τ−1), ±1, ±(2τ − 1))
<p>with an even number of minuses in the choices for '±', where τ = (1+√5)/2 is the <a href="/facts/Golden_ratio/anloSRmD">golden ratio</a> (sometimes written φ).
</p>

<ul><li>Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", <i><a href="/facts/Mathematical_Proceedings_of_the_Cambridge_Philosophical_Society/KUUzcS7S">Mathematical Proceedings of the Cambridge Philosophical Society</a></i>, 79 (3): 447–457, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1017%2FS0305004100052440">10.1017/S0305004100052440</a>, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0397554">0397554</a>.</li></ul>

Compound of five truncated tetrahedra open-in-new

Compound of five truncated tetrahedra