Digonal-square prismantiprismoid

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Digonal-square prismantiprismoid
Bowers style acronymDispap
Coxeter diagramx4s2s4o ()
Cells4 tetragonal disphenoids, 8 wedges, 4 rectangular trapezoprisms
Faces16 isosceles triangles, 16 isosceles trapezoids, 4+4 rectangles
Vertex figureMirror-symmetric notch
Measures (as derived from unit-edge square-octagonal duoprism)
Edge lengthsShort edges of rectangles (8): 1
 Side edges (8+16):
 Long edges of rectangles (8):
Central density1
Related polytopes
DualDigonal-square tegmantitegmoid
Abstract & topological properties
Euler characteristic0
Symmetry(B2×B2)/2, order 32

The digonal-square prismantiprismoid or dispap, also known as the edge-snub digonal-square duoprism, 2-4 prismantiprismoid, digonal duoexpandoprism, or digonal duotruncatoalterprism, is a convex isogonal polychoron and the first member of the duoexpandoprism, duotruncatoprism, and duotruncatoalterprism families. It consists of 4 rectangular trapezoprisms, 4 tetragonal disphenoids, and 8 wedges. 1 tetrgonal disphenoid, 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 square-octagonal duoprism so that the 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.

A variant with regular tetrahedra and squares can be vertex-inscribed into a rectified tesseract.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.36603.

Vertex coordinates[edit | edit source]

The vertices of a digonal-square prismantiprismoid, assuming that the tetragonal disphenoids are regular and are connected by squares of edge length 1, centered at the origin, are given by:

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by:

An additional variant based on a unit square-octagonal duoprism has vertices given by: