Snub penteract

The snub penteract or snan is a convex isogonal polyteron obtained through the process of alternating the great cellated penteractitriacontaditeron. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{24+9\sqrt2}{23}}$$ ≈ 1:1.26367.

Vertex coordinates
Coordinates for the vertices of an optimized snub penteract. using the ratio method, are given by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes, of:
 * ($\sqrt{4-2√2}$/4, $\sqrt{4+2√2}$/4, $\sqrt{60+18√2+24√6+3√2}$/12, $\sqrt{132+18√2+48√6+3√2}$/12, $\sqrt{28+2√2+8√6+3√2}$/4).