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

Overview

Group: SmallGroup(40,13)
Rank: 3
Schläfli Type: {10,2}
Vertices, edges, …: 10, 10, 2
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
Self-Petrie

Related Polytopes

Constructions

Facet of

Vertex figure of

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

Quotients maximal quotients in bold

2-fold

{5,2}*20

5-fold

{2,2}*8

Covers minimal covers in bold

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Representations

Permutation Representation (GAP)

s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (11,12);;
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*s2*s0*s2, s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

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