Polytope of Type {4,38} with group SmallGroup(304,31)

Overview

Group: SmallGroup(304,31)
Rank: 3
Schläfli Type: {4,38}
Vertices, edges, …: 4, 76, 38
Order of s₀s₁s₂: 76
Order of s₀s₁s₂s₁: 2
Also known as: {4,38|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

{2,38}*152

4-fold

{2,19}*76

19-fold

{4,2}*16

38-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 := (39,58)(40,59)(41,60)(42,61)(43,62)(44,63)(45,64)(46,65)(47,66)(48,67)(49,68)(50,69)(51,70)(52,71)(53,72)(54,73)(55,74)(56,75)(57,76);;
s1 := ( 1,39)( 2,57)( 3,56)( 4,55)( 5,54)( 6,53)( 7,52)( 8,51)( 9,50)(10,49)(11,48)(12,47)(13,46)(14,45)(15,44)(16,43)(17,42)(18,41)(19,40)(20,58)(21,76)(22,75)(23,74)(24,73)(25,72)(26,71)(27,70)(28,69)(29,68)(30,67)(31,66)(32,65)(33,64)(34,63)(35,62)(36,61)(37,60)(38,59);;
s2 := ( 1, 2)( 3,19)( 4,18)( 5,17)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(20,21)(22,38)(23,37)(24,36)(25,35)(26,34)(27,33)(28,32)(29,31)(39,40)(41,57)(42,56)(43,55)(44,54)(45,53)(46,52)(47,51)(48,50)(58,59)(60,76)(61,75)(62,74)(63,73)(64,72)(65,71)(66,70)(67,69);;
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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(76)!(39,58)(40,59)(41,60)(42,61)(43,62)(44,63)(45,64)(46,65)(47,66)(48,67)(49,68)(50,69)(51,70)(52,71)(53,72)(54,73)(55,74)(56,75)(57,76);
s1 := Sym(76)!( 1,39)( 2,57)( 3,56)( 4,55)( 5,54)( 6,53)( 7,52)( 8,51)( 9,50)(10,49)(11,48)(12,47)(13,46)(14,45)(15,44)(16,43)(17,42)(18,41)(19,40)(20,58)(21,76)(22,75)(23,74)(24,73)(25,72)(26,71)(27,70)(28,69)(29,68)(30,67)(31,66)(32,65)(33,64)(34,63)(35,62)(36,61)(37,60)(38,59);
s2 := Sym(76)!( 1, 2)( 3,19)( 4,18)( 5,17)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(20,21)(22,38)(23,37)(24,36)(25,35)(26,34)(27,33)(28,32)(29,31)(39,40)(41,57)(42,56)(43,55)(44,54)(45,53)(46,52)(47,51)(48,50)(58,59)(60,76)(61,75)(62,74)(63,73)(64,72)(65,71)(66,70)(67,69);
poly := sub<Sym(76)|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*s1*s2*s1*s2 >;

References