Second noble kisombreroidal icositetrahedron

The Second noble kisombreroidal icositetrahedron is a noble polyhedron. Its 24 congruent faces are irregular pentagons meeting at congruent order-5 vertices. It is a faceting of an isogonal non-uniform snub cubic hull.

The ratio between the longest and shortest edges is 1:2.28455.

Vertex coordinates
This polyhedron has coordinates given by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes, of


 * (1, a, b),

where


 * $$a = \sqrt[3]{1+\sqrt{\frac{19}{27}}}+\sqrt[3]{1-\sqrt{\frac{19}{27}}}+1\approx2.76929$$

is the real root of $$x^3-3x^2+x-1$$, and


 * $$b=\sqrt[3]{\frac{514}{27}+\sqrt{\frac{76}{27}}}+\sqrt[3]{\frac{514}{27}-\sqrt{\frac{76}{27}}}+\frac{7}{3}\approx7.66898$$

is the real root of $$x^3-7x^2-5x-1$$.