Snub square antiprismatic honeycomb

Snub square antiprismatic honeycomb
Rank	4
Type	Isogonal
Space	Euclidean
Notation
Coxeter diagram	s∞o2s4s4o
Elements
Cells	4N sphenoids, N tetragonal disphenoids, N square gyroprisms
Faces	8N scalene triangles, 4N isosceles triangles, N squares
Edges	N+2N+4N+4N
Vertices	2N
Vertex figure	Triangular-pentagonal orthobigyrowedge
Measures (based on truncated square prismatic honeycomb of edge length 1)
Edge lengths	Diagonals of original squares (N+2N+4N): ${\sqrt {2}}\approx 1.41421$
	Edges of octagons (N): ${\sqrt {2+{\sqrt {2}}}}\approx 1.84776$
Related polytopes
Dual	Cairo pentagonal antitegmatic honeycomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	(R3❘W2)+
Convex	Yes
Nature	Tame

The snub square antiprismatic honeycomb is an isogonal honeycomb that consists of square gyroprisms, tetragonal disphenoids, and sphenoids. 4 square gyroprisms, 2 tetragonal disphenoids, and 8 irregular tetrahedra join at each vertex. It can be obtained through the process of alternating the truncated square prismatic honeycomb. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\frac {\sqrt {5}}{2}}$ ≈ 1:1.11803.

External links

• Klitzing, Richard. "s∞o2s4s4o".