Edge-snub trihexagonal prismatic honeycomb

Edge-snub trihexagonal prismatic honeycomb
Rank	4
Type	Isogonal
Space	Euclidean
Notation
Coxeter diagram	s∞o2s3s6x
Elements
Cells	3N wedges, 2N triangular gyroprisms, N ditrigonal trapezoprisms
Faces	12N scalene triangles, 2N triangles, 6N isosceles trapezoids, 3N rectangles, N ditrigons
Edges	3N+3N+6N+6N+6N
Vertices	6N
Vertex figure	Kite-hexagonal orthonotch
Measures (based on great rhombitrihexagonal prismatic honeycomb of edge length 1)
Edge lengths	Remaining original eddges (3N): 1
	Diagonals of original squares (6N+6N): ${\sqrt {2}}\approx 1.41421$
	Edges of triangles (6N): ${\sqrt {3}}\approx 1.73205$
	Long edges of ditrigons (N): ${\frac {{\sqrt {2}}+{\sqrt {6}}}{2}}\approx 1.93185$
Related polytopes
Dual	Trihexagonal isosceles trapezoidal-hexagonal orthowedge honeycomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	P3❘W2)+
Convex	Yes
Nature	Tame

The edge-snub trihexagonal prismatic honeycomb is an isogonal honeycomb that consists of ditrigonal trapezoprisms, triangular gyroprisms, and wedges. 2 ditrigonal trapezoprisms, 2 triangular gyroprisms, and 6 wedges join at each vertex. It can be obtained as a subsymmetrical faceting of the great rhombitrihexagonal prismatic honeycomb, faceting the dodecagons into ditrigons. However, it cannot be made uniform.

The sectioning facet underneath the alternatingly omitted edge of the prismatic pre-image honeycomb clearly is bistratic (the biwedge), which are subdivided into two wedges.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:a ≈ 1:1.32682, where a is the second largest real root of 7x⁴-10x³-10x²+10x+6.

External links

• Klitzing, Richard. "s∞o2s3s6x".