Overview
- Group
- SmallGroup(576,8262)
- Rank
- 5
- Schläfli Type
- {2,4,18,2}
- Vertices, edges, …
- 2, 4, 36, 18, 2
- Order of s0s1s2s3s4
- 18
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
Covers minimal covers in bold
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74);; s2 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(15,31)(16,33)(17,32)(18,34)(19,27)(20,29)(21,28)(22,30)(23,35)(24,37)(25,36)(26,38)(40,41)(43,47)(44,49)(45,48)(46,50)(51,67)(52,69)(53,68)(54,70)(55,63)(56,65)(57,64)(58,66)(59,71)(60,73)(61,72)(62,74);; s3 := ( 3,51)( 4,52)( 5,54)( 6,53)( 7,59)( 8,60)( 9,62)(10,61)(11,55)(12,56)(13,58)(14,57)(15,39)(16,40)(17,42)(18,41)(19,47)(20,48)(21,50)(22,49)(23,43)(24,44)(25,46)(26,45)(27,67)(28,68)(29,70)(30,69)(31,63)(32,64)(33,66)(34,65)(35,71)(36,72)(37,74)(38,73);; s4 := (75,76);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(76)!(1,2); s1 := Sym(76)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74); s2 := Sym(76)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(15,31)(16,33)(17,32)(18,34)(19,27)(20,29)(21,28)(22,30)(23,35)(24,37)(25,36)(26,38)(40,41)(43,47)(44,49)(45,48)(46,50)(51,67)(52,69)(53,68)(54,70)(55,63)(56,65)(57,64)(58,66)(59,71)(60,73)(61,72)(62,74); s3 := Sym(76)!( 3,51)( 4,52)( 5,54)( 6,53)( 7,59)( 8,60)( 9,62)(10,61)(11,55)(12,56)(13,58)(14,57)(15,39)(16,40)(17,42)(18,41)(19,47)(20,48)(21,50)(22,49)(23,43)(24,44)(25,46)(26,45)(27,67)(28,68)(29,70)(30,69)(31,63)(32,64)(33,66)(34,65)(35,71)(36,72)(37,74)(38,73); s4 := Sym(76)!(75,76); poly := sub<Sym(76)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;