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

Overview

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

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

3-fold

{4,12}*96a

4-fold

{2,18}*72

6-fold

8-fold

{2,9}*36

9-fold

{4,4}*32

12-fold

{2,6}*24

18-fold

24-fold

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

References