Square scalene

The square scalene, square pyramidal pyramid, or squasc, is a CRF segmentochoron (designated K-4.4 on Richard Klitzing's list). It consists of a square pyramid connected to five other pyramids that meet at an external point: another square pyramid and four triangular pyramids.

Apart from being a point atop square pyramid, it has alternate segmentochoron representations as a dyad atop tetrahedron, dyad atop perpendicular square and triangle atop inclined triangle.

It can be viewed as a quarter of the hexadecachoron or a half of the octahedral pyramid.

Vertex coordinates
The vertices of a square scalene with unit edge length are given by: and all permutations, in the first 2 coordinates, of
 * (0, 0, 0, $\sqrt{2}$/2),
 * (0, 0, $\sqrt{2}$/2, 0),
 * (±$\sqrt{2}$/2, 0, 0, 0).

Representations
The square pyramidal pyramid has the following Coxeter diagrams:
 * oox4ooo&#x (point atop square pyramid)
 * oox oox&#x
 * xo ox4oo&#x (line in dim. 3,4 and square in dim. 1,2)
 * xo ox ox&#x
 * xoo oxx&#x