Small rhombated dodecahedral honeycomb

Small rhombated dodecahedral honeycomb
Rank	4
Type	Uniform, compact
Space	Hyperbolic
Notation
Bowers style acronym	Sriddoh
Coxeter diagram	x5o3x4o ()
Elements
Cells	15N cubes, 5N cuboctahedra, 2N small rhombicosidodecahedra
Faces	40N triangles, 30N+60N squares, 12N pentagons
Edges	60N+120N
Vertices	60N
Vertex figure	Rectangular wedge, edge lengths 1 (two edges of base), (1+√5)/2 (top edge), and √2 (remaining edges)
Measures (edge length 1)
Circumradius
Related polytopes
Army	Sriddoh
Regiment	Sriddoh
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	[5,3,4]
Convex	Yes

The small rhombated dodecahedral honeycomb, also called the cantellated dodecahedral honeycomb, is a compact uniform tiling of 3D hyperbolic space. 2 cubes (as square prisms), 1 cuboctahedron, and 2 small rhombicosidodecahedra meet at each vertex. As the name suggests, it can be derived by cantellation of the dodecahedral honeycomb.

Representations[edit | edit source]

A small rhombated dodecahedral honeycomb has the following Coxeter diagrams:

v t e truncations
Name	OBSA	Schläfli symbol	CD diagram	Image
Dodecahedral honeycomb	doehon	${5,3,4}$
Rectified dodecahedral honeycomb	riddoh	r ${5,3,4}$
Rectified order-5 cubic honeycomb	ripech	r ${4,3,5}$
Order-5 cubic honeycomb	pechon	${4,3,5}$
Truncated dodecahedral honeycomb	tiddoh	t ${5,3,4}$
Small rhombated dodecahedral honeycomb	sriddoh	rr ${5,3,4}$
Small prismated dodecahedral honeycomb	sidpicdoh	t_0,3 ${5,3,4}$
Cubic-dodecahedral honeycomb	ciddoh	2t ${5,3,4}$
Small rhombated order-5 cubic honeycomb	sripech	rr ${4,3,5}$
Truncated order-5 cubic honeycomb	tipech	t ${4,3,5}$
Great rhombated dodecahedral honeycomb	griddoh	tr ${5,3,4}$
Prismatorhombated order-5 cubic honeycomb	pripech	t_0,1,3 ${5,3,4}$
Prismatorhombated dodecahedral honeycomb	priddoh	t_0,1,3 ${4,3,5}$
Great rhombated order-5 cubic honeycomb	gripech	tr ${4,3,5}$
Great prismated dodecahedral honeycomb	gidpicdoh	t_0,1,2,3 ${5,3,4}$
Order-5 demicubic honeycomb	phachon	s ${5,3,4}$
Truncated order-5 demicubic honeycomb	tophach
Small rhombated order-5 demicubic honeycomb	sirphach
Great rhombated order-5 demicubic honeycomb	girphach

v t e truncations
Name	OBSA	CD diagram	Image
Dodecahedral honeycomb	doehon
Rectified dodecahedral honeycomb	riddoh
Alternated order-5 cubic honeycomb	apech
Truncated dodecahedral honeycomb	tiddoh
Runcic order-5 cubic honeycomb	birapech
Cantic order-5 cubic honeycomb	tapech
Rectified order-5 cubic honeycomb	ripech
Runcicantic order-5 cubic honeycomb	bitapech
Small rhombated dodecahedral honeycomb	sriddoh
Cubic-dodecahedral honeycomb	ciddoh
Great rhombated dodecahedral honeycomb	griddoh