Edge-snub square prismatic honeycomb
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Edge-snub square prismatic honeycomb | |
---|---|
Rank | 4 |
Type | Isogonal |
Space | Euclidean |
Notation | |
Coxeter diagram | s∞o2s4s4x |
Elements | |
Cells | 2N wedges, N rectangular trapezoprisms, N square gyroprisms |
Faces | 8N scalene triangles, 4N isosceles trapezoids, N+2N rectangles, N squares |
Edges | 2N+2N+4N+4N+4N |
Vertices | 4N |
Vertex figure | Triangular-pentagonal orthobigyrowedge |
Measures (based on truncated square prismatic honeycomb of edge length 1) | |
Edge lengths | Remaining original edges (3N): 1 |
Diagonals of original squares (4N+4N): | |
Diagonals of original ditetragons (4N): | |
Long edges of rectangles (2N): | |
Related polytopes | |
Dual | Square isosceles trapezoidal-hexagonal orthowedge honeycomb |
Abstract & topological properties | |
Orientable | Yes |
Properties | |
Symmetry | (R3+❘W2)+ |
Convex | Yes |
Nature | Tame |
The edge-snub square prismatic honeycomb is an isogonal honeycomb that consists of square gyroprisms, rectangular trapezoprisms, and wedges. 2 square gyroprisms, 2 rectangular trapezoprisms, and 6 wedges join at each vertex. It can be obtained as a subsymmetrical faceting of the truncated square prismatic honeycomb, faceting half of the octagons into rectangles. 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 ≈ 1:1.29180, where a is the second largest real root of 5x4-8x3-6x2+8x+3.
External links[edit | edit source]
- Klitzing, Richard. "s∞o2s4s4x".