List of regular polytopes and compounds
Tessellations of hyperbolic 3-space
There are ten flat regular honeycombs of hyperbolic 3-space: (previously listed above as tessellations) 4 are compact: {3,5,3}, {4,3,5}, {5,3,4}, and {5,3,5} while 6 are paracompact: {3,3,6}, {6,3,3}, {3,4,4}, {4,4,3}, {3,6,3}, {4,3,6}, {6,3,4}, {4,4,4}, {5,3,6}, {6,3,5}, and {6,3,6}.

List of regular polytopes and compounds

Section Title: Tessellations of hyperbolic 3-space
Table Section Text: There are ten flat regular honeycombs of hyperbolic 3-space: (previously listed above as tessellations) 4 are compact: {3,5,3}, {4,3,5}, {5,3,4}, and {5,3,5} while 6 are paracompact: {3,3,6}, {6,3,3}, {3,4,4}, {4,4,3}, {3,6,3}, {4,3,6}, {6,3,4}, {4,4,4}, {5,3,6}, {6,3,5}, and {6,3,6}.

Name	Schläfli Symbol {p,q,r}	Coxeter	Cell type {p,q}	Face type {p}	Edge figure {r}	Vertex figure {q,r}	χ	Dual

Order-6 tetrahedral honeycomb	{3,3,6}	{3,3}	{3}	{6}	{3,6}	0	{6,3,3}

Hexagonal tiling honeycomb	{6,3,3}	{6,3}	{6}	{3}	{3,3}	0	{3,3,6}

Order-4 octahedral honeycomb	{3,4,4}	{3,4}	{3}	{4}	{4,4}	0	{4,4,3}

Square tiling honeycomb	{4,4,3}	{4,4}	{4}	{3}	{4,3}	0	{3,3,4}

Triangular tiling honeycomb	{3,6,3}	{3,6}	{3}	{3}	{6,3}	0	Self-dual

Order-6 cubic honeycomb	{4,3,6}	{4,3}	{4}	{4}	{3,4}	0	{6,3,4}

Order-4 hexagonal tiling honeycomb	{6,3,4}	{6,3}	{6}	{4}	{3,4}	0	{4,3,6}

Order-4 square tiling honeycomb	{4,4,4}	{4,4}	{4}	{4}	{4,4}	0	{4,4,4}

Order-6 dodecahedral honeycomb	{5,3,6}	{5,3}	{5}	{5}	{3,5}	0	{6,3,5}

Order-5 hexagonal tiling honeycomb	{6,3,5}	{6,3}	{6}	{5}	{3,5}	0	{5,3,6}

Order-6 hexagonal tiling honeycomb	{6,3,6}	{6,3}	{6}	{6}	{3,6}	0	Self-dual

Sentence(s)

Order-6 tetrahedral honeycomb is one regular hyperbolic honeycomb in 3-space.

final_sentence: Order-6 tetrahedral honeycomb is one regular hyperbolic honeycomb in 3-space.