Square-square prismantiprismoid

The square-square prismantiprismoid or sispap, also known as the edge-snub square-square duoprism or 4-4 prismantiprismoid, is a convex isogonal polychoron that consists of 4 square antiprisms, 4 square prisms, 8 rectangular trapezoprisms, and 16 wedges. 1 square prism, 1 square antiprism, 2 rectangular trapezoprisms, and 3 wedges join at each vertex. It can be obtained through the process of alternating one class of edges of the octagonal duoprism so that one ring of octagons become rectangles. However, it cannot be made uniform, as it generally has 4 edge lengths, which can be minimized to no fewer than 2 different sizes.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{3+\sqrt2+\sqrt{32+13\sqrt2}}{7}$$ ≈ 1:1.64463.

Vertex coordinates
The vertices of a square-square prismantiprismoid based on an octagonal duoprism of edge length 1, centered at the origin, are given by:


 * $$\left(±\frac{\sqrt{2+\sqrt2}}{2},\,±\frac{\sqrt{2+\sqrt2}}{2},\,±\frac12,\,±\frac{1+\sqrt2}{2}\right),$$
 * $$\left(±\sqrt{\frac{2+\sqrt2}{2}},\,0,\,±\frac{1+\sqrt2}{2},\,±\frac12\right),$$
 * $$\left(0,\,±\sqrt{\frac{2+\sqrt2}{2}},\,±\frac{1+\sqrt2}{2},\,±\frac12\right).$$