|Bowers style acronym||Dispap|
|Coxeter diagram||x4s2s4o ()|
|Cells||4 tetragonal disphenoids, 8 wedges, 4 rectangular trapezoprisms|
|Faces||16 isosceles triangles, 16 isosceles trapezoids, 4+4 rectangles|
|Vertex figure||Mirror-symmetric notch|
|Measures (as derived from unit-edge square-octagonal duoprism)|
|Edge lengths||Short edges of rectangles (8): 1|
|Side edges (8+16):|
|Long edges of rectangles (8):|
|Abstract & topological properties|
|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: