Polytope of Type {2,10} with group SmallGroup(40,13) - Atlas of Small Regular Polytopes

Overview

Group: SmallGroup(40,13)
Rank: 3
Schläfli Type: {2,10}
Vertices, edges, …: 2, 10, 10
Order of s₀s₁s₂: 10
Order of s₀s₁s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

{2,10,2} ·80
{2,10,4} ·160
{2,10,5} ·200
{2,10,3} ·240
{2,10,3} ·240
{2,10,5} ·240
{2,10,5} ·240
{2,10,6} ·240
{2,10,8} ·320
{2,10,4} ·400
{2,10,10} ·400
{2,10,10} ·400
{2,10,10} ·400
{2,10,12} ·480
{2,10,4} ·480
{2,10,4} ·480
{2,10,6} ·480
{2,10,6} ·480
{2,10,3} ·480
{2,10,5} ·480
{2,10,6} ·480
{2,10,6} ·480
{2,10,6} ·480
{2,10,6} ·480
{2,10,10} ·480
{2,10,10} ·480
{2,10,10} ·480
{2,10,10} ·480
{2,10,14} ·560
{2,10,3} ·600
{2,10,6} ·600
{2,10,15} ·600
{2,10,16} ·640
{2,10,5} ·640
{2,10,4} ·640
{2,10,4} ·640
{2,10,5} ·640
{2,10,18} ·720
{2,10,3} ·720
{2,10,15} ·720
{2,10,20} ·800
{2,10,20} ·800
{2,10,20} ·800
{2,10,4} ·800
{2,10,22} ·880
{2,10,24} ·960
{2,10,6} ·960
{2,10,4} ·960
{2,10,4} ·960
{2,10,12} ·960
{2,10,12} ·960
{2,10,12} ·960
{2,10,12} ·960
{2,10,20} ·960
{2,10,20} ·960
{2,10,4} ·960
{2,10,6} ·960
{2,10,6} ·960
{2,10,10} ·960
{2,10,25} ·1000
{2,10,5} ·1000
{2,10,10} ·1000
{2,10,26} ·1040
{2,10,28} ·1120
{2,10,5} ·1200
{2,10,15} ·1200
{2,10,6} ·1200
{2,10,6} ·1200
{2,10,12} ·1200
{2,10,30} ·1200
{2,10,30} ·1200
{2,10,30} ·1200
{2,10,32} ·1280
{2,10,5} ·1280
{2,10,8} ·1280
{2,10,8} ·1280
{2,10,8} ·1280
{2,10,8} ·1280
{2,10,10} ·1280
{2,10,10} ·1280
{2,10,10} ·1280
{2,10,4} ·1280
{2,10,4} ·1280
{2,10,10} ·1280
{2,10,34} ·1360
{2,10,35} ·1400
{2,10,36} ·1440
{2,10,3} ·1440
{2,10,4} ·1440
{2,10,5} ·1440
{2,10,8} ·1440
{2,10,8} ·1440
{2,10,10} ·1440
{2,10,10} ·1440
{2,10,6} ·1440
{2,10,12} ·1440
{2,10,3} ·1440
{2,10,6} ·1440
{2,10,6} ·1440
{2,10,15} ·1440
{2,10,30} ·1440
{2,10,30} ·1440
{2,10,38} ·1520
{2,10,40} ·1600
{2,10,40} ·1600
{2,10,40} ·1600
{2,10,8} ·1600
{2,10,21} ·1680
{2,10,35} ·1680
{2,10,42} ·1680
{2,10,44} ·1760
{2,10,9} ·1800
{2,10,18} ·1800
{2,10,45} ·1800
{2,10,46} ·1840
{2,10,48} ·1920
{2,10,12} ·1920
{2,10,15} ·1920
{2,10,8} ·1920
{2,10,8} ·1920
{2,10,24} ·1920
{2,10,24} ·1920
{2,10,24} ·1920
{2,10,24} ·1920
{2,10,40} ·1920
{2,10,40} ·1920
{2,10,4} ·1920
{2,10,12} ·1920
{2,10,12} ·1920
{2,10,20} ·1920
{2,10,6} ·1920
{2,10,8} ·1920
{2,10,8} ·1920
{2,10,12} ·1920
{2,10,12} ·1920
{2,10,20} ·1920
{2,10,6} ·1920
{2,10,10} ·1920
{2,10,4} ·2000
{2,10,20} ·2000
{2,10,20} ·2000
{2,10,20} ·2000
{2,10,20} ·2000
{2,10,50} ·2000
{2,10,50} ·2000
{2,10,10} ·2000
{2,10,10} ·2000
{2,10,10} ·2000
{2,10,20} ·2000
{2,10,10} ·2000

Vertex figure of

Quotients maximal quotients in bold

2-fold

{2,5}*20

5-fold

{2,2}*8

Covers minimal covers in bold

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Representations

Permutation Representation (GAP)

s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(12)!(1,2);
s1 := Sym(12)!( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(12)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12);
poly := sub<Sym(12)|s0,s1,s2>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;