Noble octagrammic icositetrahedron

The noble octagrammic icositetrahedron is a noble polyhedron. Its 24 congruent faces are mirror-symmetric octagrams meeting at congruent order-4 vertices. It is a faceting of a semi-uniform great rhombicuboctahedral convex hull.

The ratio between the longest and shortest edges is 1:a ≈ 1:1.19166, where a is the positive real root of 27a6-47a4+13a2-1.

Vertex coordinates
This polyhedron's vertex coordinates are given by all permutations and sign changes of


 * (1, a, b),

where


 * $$a=\frac{\sqrt[3]{188+12\sqrt{93}}+\sqrt[3]{188-12\sqrt{93}}+5}{6}$$, and
 * $$b=\frac{\sqrt[3]{188+12\sqrt{93}}+\sqrt[3]{188-12\sqrt{93}}+\sqrt[3]{116+12\sqrt{93}}+\sqrt[3]{116-12\sqrt{93}}+7}{6}$$.