Edge-snub trihexagonal prismatic honeycomb

{{Infobox polytope The edge-snub triangular 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.
 * image =
 * dim = 4
 * type = Isogonal
 * space=Euclidean
 * obsa =
 * cells = 3N wedges, 2N triangular gyroprisms, N ditrigonal trapezoprisms
 * faces = 2N triangles, 12N isosceles triangles, 3N rectangles, 6N isosceles trapezoids, 2N triangles, N ditrigons
 * edges = 3N+3N+6N+6N+6N
 * vertices = 6N
 * verf = Kite-hexagonal orthonotch
 * coxeter = s∞o2s3s6x
 * symmetry = P3❘W2+
 * custom_measure = (based on great rhombitrihexagonal prismatic honeycomb of edge length 1)
 * el = Remaining original eddges (3N): 1
 * el2 = Diagonals of original squares (6N+6N): $$\sqrt2 ≈ 1.41421$$
 * el3 = Edges of triangles (6N): $$\sqrt3 ≈ 1.73205$$
 * el4 = Long edges of ditrigons (N): $$\frac{\sqrt2+\sqrt6}{2] ≈ 1.93185$$
 * dual=Isosceles trapezoidal-hexagonal orthowedge honeycomb
 * conv = Yes
 * orientable = Yes
 * nat = Tame}}

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

Optimization
Since the edge-snub triangular prismatic honeycomb has three variations in its highest symmetry, optimization gives the following edge lengths as:


 * $$1$$
 * $$root(7x^4-10x^3-10x^2+10x+6, 3) ≈ 1.3268170959556440919234783$$

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