Square double antiprismoid

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Square double antiprismoid
Rank4
TypeIsogonal
Notation
Bowers style acronymSquidiap
Elements
Cells128 sphenoids, 64 tetragonal disphenoids, 16 square antiprisms
Faces64+128+256 isosceles triangles, 16 squares
Edges64+128+128
Vertices64
Vertex figureSphenocorona
Measures (for variant with unit uniform square antiprisms)
Edge lengthsLacing edges of disphenoids (128):
 Base edges of antiprisms (64): 1
 Side edges of antiprisms (128): 1
Circumradius
Central density1
Related polytopes
ArmySquidiap
RegimentSquidiap
DualSquare double antitegmoid
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(8)+≀S2×2, order 256
ConvexYes
NatureTame

The square double antiprismoid or squidiap is a convex isogonal polychoron and the third member of the double antiprismoid family. It consists of 16 square antiprisms, 64 tetragonal disphenoids, and 128 sphenoids. 2 square antiprisms, 4 tetragonal disphenoids, and 8 sphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal square-square duoantiprisms or by alternating the octagonal ditetragoltriate. However, it cannot be made uniform. It is the first in an infinite family of isogonal square antiprismatic swirlchora.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.07072. For this variant the edges of the squares of the inscribed duoantiprisms have ratio 1: ≈ 1:1.70711. A variant with uniform square antiprisms also exists; this variant is based on a duoantiprism based on squares with edge length ratio 1: ≈ 1:1.55377.

Vertex coordinates[edit | edit source]

The vertices of a square double antiprismoid, assuming that the square antiprisms are uniform 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: