# Edge-snub trihexagonal prismatic honeycomb

Edge-snub trihexagonal prismatic honeycomb
Rank4
TypeIsogonal
SpaceEuclidean
Notation
Coxeter diagrams∞o2s3s6x
Elements
Cells3N wedges, 2N triangular gyroprisms, N ditrigonal trapezoprisms
Faces12N scalene triangles, 2N triangles, 6N isosceles trapezoids, 3N rectangles, N ditrigons
Edges3N+3N+6N+6N+6N
Vertices6N
Vertex figureKite-hexagonal orthonotch
Measures (based on great rhombitrihexagonal prismatic honeycomb of edge length 1)
Edge lengthsRemaining original eddges (3N): 1
Diagonals of original squares (6N+6N): ${\displaystyle {\sqrt {2}}\approx 1.41421}$
Edges of triangles (6N): ${\displaystyle {\sqrt {3}}\approx 1.73205}$
Long edges of ditrigons (N): ${\displaystyle {\frac {{\sqrt {2}}+{\sqrt {6}}}{2}}\approx 1.93185}$
Related polytopes
DualTrihexagonal isosceles trapezoidal-hexagonal orthowedge honeycomb
Abstract & topological properties
OrientableYes
Properties
SymmetryP3❘W2)+
ConvexYes
NatureTame

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.