Triangular-square duoprism

The triangular-square duoprism or tisdip, also known as the 3-4 duoprism, is a uniform duoprism that consists of 3 cubes and 4 triangular prisms, with two of each meeting at each vertex. It can also be seen as a prism based on the triangular prism, which makes it a convex segmentochoron (designated K-4.18 on Richard Klitzing's) list in two different ways, as a prism of a triangular prism or square atop cube.

Vertex coordinates
Coordinates for the vertices of a triangular-square duoprism of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,±\frac12\right).$$

Representations
A triangular-square duoprism has the following Coxeter diagrams:


 * x3o x4o (full symmetry)
 * x x x3o (A2×A1×A1 symmetry, triangular prismatic prism)
 * xx xx3oo&#x (A2×A1 axial, prism of triangular prism)
 * ox xx4oo&#x (BC2×A1 axial, square atop cube)
 * ox xx xx&#x (A1×A1×A1 symmetry, as above with rectangles instead of squares)
 * xxx3ooo oqo&#xt (A2×A1 axial, triangle-first)
 * xxx xxx&#x (A1×A1 symmetry, 3 squares seen separately)