Kisrhombille tiling

Kisrhombille tiling
Rank	3
Type	Uniform dual
Space	Euclidean
Notation
Coxeter diagram	m6m3m ()
Elements
Faces	12N scalene triangles
Edges	6N+6N+6N
Vertices	N+2N+3N
Vertex figure	N dodecagons, 2N hexagons, 3N squares
Related polytopes
Dual	Great rhombitrihexagonal tiling
Conjugate	Great kisrhombille tiling
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	V3
Convex	Yes
Nature	Tame

The kisrhombille tiling is an isohedral tiling with scalene triangles for faces, joining 4, 6, or 12 to a vertex. It is the dual of the uniform great rhombitrihexagonal tiling.

Each face of this tiling is a right triangle. If the shortest edges have length 1, the medium edges have length ${\sqrt {2}}\approx 1.41421$ and the longest edges have length ${\sqrt {3}}\approx 1.73205$. These triangles have angles measuring 30°, 60°, and 90°.

External links

• Wikipedia contributors. "Kisrhombille tiling".