Polytope of Type {36,4} with group SmallGroup(288,92)

Overview

Group: SmallGroup(288,92)
Rank: 3
Schläfli Type: {36,4}
Vertices, edges, …: 36, 72, 4
Order of s₀s₁s₂: 36
Order of s₀s₁s₂s₁: 2
Also known as: {36,4|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

3-fold

{12,4}*96a

4-fold

{18,2}*72

6-fold

8-fold

{9,2}*36

9-fold

{4,4}*32

12-fold

{6,2}*24

18-fold

24-fold

{3,2}*12

36-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 2, 3)( 4, 8)( 5, 7)( 6, 9)(11,12)(13,17)(14,16)(15,18)(20,21)(22,26)(23,25)(24,27)(29,30)(31,35)(32,34)(33,36)(37,55)(38,57)(39,56)(40,62)(41,61)(42,63)(43,59)(44,58)(45,60)(46,64)(47,66)(48,65)(49,71)(50,70)(51,72)(52,68)(53,67)(54,69);;
s1 := ( 1,40)( 2,42)( 3,41)( 4,37)( 5,39)( 6,38)( 7,44)( 8,43)( 9,45)(10,49)(11,51)(12,50)(13,46)(14,48)(15,47)(16,53)(17,52)(18,54)(19,58)(20,60)(21,59)(22,55)(23,57)(24,56)(25,62)(26,61)(27,63)(28,67)(29,69)(30,68)(31,64)(32,66)(33,65)(34,71)(35,70)(36,72);;
s2 := (37,46)(38,47)(39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(55,64)(56,65)(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(72)!( 2, 3)( 4, 8)( 5, 7)( 6, 9)(11,12)(13,17)(14,16)(15,18)(20,21)(22,26)(23,25)(24,27)(29,30)(31,35)(32,34)(33,36)(37,55)(38,57)(39,56)(40,62)(41,61)(42,63)(43,59)(44,58)(45,60)(46,64)(47,66)(48,65)(49,71)(50,70)(51,72)(52,68)(53,67)(54,69);
s1 := Sym(72)!( 1,40)( 2,42)( 3,41)( 4,37)( 5,39)( 6,38)( 7,44)( 8,43)( 9,45)(10,49)(11,51)(12,50)(13,46)(14,48)(15,47)(16,53)(17,52)(18,54)(19,58)(20,60)(21,59)(22,55)(23,57)(24,56)(25,62)(26,61)(27,63)(28,67)(29,69)(30,68)(31,64)(32,66)(33,65)(34,71)(35,70)(36,72);
s2 := Sym(72)!(37,46)(38,47)(39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(55,64)(56,65)(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72);
poly := sub<Sym(72)|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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References