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...[[List of regular polytopes#Tessellations of hyperbolic 3-space|Hyperbolic regular honeycomb]]<BR>[[Paracompact uniform honeycomb]] |bgcolor=#e7dcc3|Properties||Regular, [[Quasiregular honeycomb|quasiregular]] ...

{{short description|Regular geometrical object in hyperbolic space}} ...[[List of regular polytopes#Tessellations of hyperbolic 3-space|Hyperbolic regular honeycomb]]<BR>[[Paracompact uniform honeycomb#.5B6.2C3.2C4.5D family|Parac ...

...[[List of regular polytopes#Tessellations of hyperbolic 3-space|Hyperbolic regular honeycomb]]<BR>[[Paracompact uniform honeycomb#.3B4.2C4.2C4.5D family|Parac |bgcolor=#e7dcc3|Properties||Regular ...

...[[List of regular polytopes#Tessellations of hyperbolic 3-space|Hyperbolic regular honeycomb]]<BR>[[Paracompact uniform honeycomb#.5B6.2C3.2C4.5D family|Parac ...]]||<!--[[File:Order-5_hexagonal_tiling_honeycomb_verf.png|100px]]<BR>-->[[regular icosahedron|icosahedron]] ...

{{Short description|Regular polytope whose 2D form is a pentagon}} ...ometry]], a '''pentagonal polytope'''<!--Glossary for Hyperspace--> is a [[regular polytope]] in ''n'' dimensions constructed from the [[Coxeter group|H<sub>' ...

...[[List of regular polytopes#Tessellations of hyperbolic 3-space|Hyperbolic regular honeycomb]]<BR>[[Paracompact uniform honeycomb#.5B4.2C4.2C4.5D family|Parac |bgcolor=#e7dcc3|Properties||Regular, [[Quasiregular honeycomb|quasiregular]] ...

...[[List of regular polytopes#Tessellations of hyperbolic 3-space|Hyperbolic regular honeycomb]]<BR>[[Paracompact uniform honeycomb#.3B6.2C6.2C3.5D family|Parac |bgcolor=#e7dcc3|Properties||Regular ...

...[[List of regular polytopes#Tessellations of hyperbolic 3-space|Hyperbolic regular honeycomb]]<BR>[[Paracompact uniform honeycomb#.5B6.2C3.2C6.5D family|Parac |bgcolor=#e7dcc3|Properties||Regular, [[Quasiregular honeycomb|quasiregular]] ...

...[[List of regular polytopes#Tessellations of hyperbolic 3-space|Hyperbolic regular honeycomb]]<BR>[[Paracompact uniform honeycomb#.6B6.2C3.2C4.5D family|Parac |bgcolor=#e7dcc3|Properties||Regular, [[Quasiregular honeycomb|quasiregular]] ...

...[[List of regular polytopes#Tessellations of hyperbolic 3-space|Hyperbolic regular honeycomb]]<BR>[[Paracompact uniform honeycomb]] |bgcolor=#e7dcc3|Properties||Regular ...

...[[List of regular polytopes#Tessellations of hyperbolic 3-space|Hyperbolic regular honeycomb]]<BR>[[Paracompact uniform honeycomb#.5B4.2C4.2C3.5D family|Parac |bgcolor=#e7dcc3|Properties||Regular ...

...[[List of regular polytopes#Tessellations of hyperbolic 3-space|Hyperbolic regular honeycomb]]<BR>[[Paracompact uniform honeycomb#.5B6.2C3.2C4.5D family|Parac |bgcolor=#e7dcc3|Properties||Regular, [[quasiregular honeycomb|quasiregular]] ...

...lyhedra]] – tessellations of the [[sphere]] – and [[toroidal polyhedra]] – tessellations of the toroids. Projective polyhedra are also referred to as '''elliptic tessellations'''<ref>{{Cite book ...

|+ Graphs of three [[List of regular polytopes#Ten Dimensions|regular]] and related [[uniform polytope]]s. == Regular 10-polytopes == ...

...reflectional Coxeter groups all with four mirrors and only the first being regular: {{CDD|node_c1|6|node|3|node|3|node}} [6,3,3], {{CDD|node_c1|3|node_c1|6|no * [[List_of_regular_polytopes#Tessellations_of_hyperbolic_3-space|Regular tessellations of hyperbolic 3-space]] ...

...url=http://archive.bridgesmathart.org/2020/bridges2020-371.html |publisher=Tessellations Publishing}}</ref> While [[rolling]] on a [[Plane (geometry)|plane]], most ...no frustum parts. The cone is created by rotating two adjacent edges of a regular polygon (and in most cases their extensions as well) around the polygon's a ...

[[File:Star polygon 9 4.png|thumb|The boundary of the regular [[Enneagram (geometry)|enneagram]] {9/4} winds around its centre 4 times, s ...blications, {{LCCN|99035678}}, {{ISBN|0-486-40919-8}} (206–214, Density of regular honeycombs in hyperbolic space)</ref> ...

...of [[Coxeter group#Properties|Coxeter group]] orders.<ref name=:0>Coxeter, Regular Polytopes, 11.8 Gossett figures in six, seven, and eight dimensions, p. 20 ...n polyhedron]], {{CDD|3node_1|3|3node|3|3node}}.<ref> Coxeter, H. S. M., ''Regular Complex Polytopes'', second edition, Cambridge University Press, (1991). p. ...

{{See also|Regular map (algebraic geometry)}} [[File:Hexagonal Hosohedron.svg|thumb|The hexagonal [[hosohedron]], a regular map on the sphere with two vertices, six edges, six faces, and 24 flags.]] ...

{{Short description|Four-dimensional analogues of the regular polyhedra in three dimensions}} [[File:Hypercube.svg|thumb|The [[tesseract]] is one of 6 convex regular 4-polytopes]] ...