Overview
- Group
- SmallGroup(1152,157863)
- Rank
- 5
- Schläfli Type
- {2,2,12,6}
- Vertices, edges, …
- 2, 2, 24, 72, 12
- Order of s0s1s2s3s4
- 6
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
24-fold
36-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := ( 5, 6)( 7, 8)( 9,14)(10,13)(11,16)(12,15)(17,18)(19,20)(21,26)(22,25)(23,28)(24,27)(29,30)(31,32)(33,38)(34,37)(35,40)(36,39)(41,42)(43,44)(45,50)(46,49)(47,52)(48,51)(53,54)(55,56)(57,62)(58,61)(59,64)(60,63)(65,66)(67,68)(69,74)(70,73)(71,76)(72,75);; s3 := ( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,33)(18,35)(19,34)(20,36)(21,29)(22,31)(23,30)(24,32)(25,37)(26,39)(27,38)(28,40)(41,45)(42,47)(43,46)(44,48)(50,51)(53,69)(54,71)(55,70)(56,72)(57,65)(58,67)(59,66)(60,68)(61,73)(62,75)(63,74)(64,76);; s4 := ( 5,53)( 6,54)( 7,56)( 8,55)( 9,61)(10,62)(11,64)(12,63)(13,57)(14,58)(15,60)(16,59)(17,41)(18,42)(19,44)(20,43)(21,49)(22,50)(23,52)(24,51)(25,45)(26,46)(27,48)(28,47)(29,65)(30,66)(31,68)(32,67)(33,73)(34,74)(35,76)(36,75)(37,69)(38,70)(39,72)(40,71);; 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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3,
s4*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s4*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(76)!(1,2); s1 := Sym(76)!(3,4); s2 := Sym(76)!( 5, 6)( 7, 8)( 9,14)(10,13)(11,16)(12,15)(17,18)(19,20)(21,26)(22,25)(23,28)(24,27)(29,30)(31,32)(33,38)(34,37)(35,40)(36,39)(41,42)(43,44)(45,50)(46,49)(47,52)(48,51)(53,54)(55,56)(57,62)(58,61)(59,64)(60,63)(65,66)(67,68)(69,74)(70,73)(71,76)(72,75); s3 := Sym(76)!( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,33)(18,35)(19,34)(20,36)(21,29)(22,31)(23,30)(24,32)(25,37)(26,39)(27,38)(28,40)(41,45)(42,47)(43,46)(44,48)(50,51)(53,69)(54,71)(55,70)(56,72)(57,65)(58,67)(59,66)(60,68)(61,73)(62,75)(63,74)(64,76); s4 := Sym(76)!( 5,53)( 6,54)( 7,56)( 8,55)( 9,61)(10,62)(11,64)(12,63)(13,57)(14,58)(15,60)(16,59)(17,41)(18,42)(19,44)(20,43)(21,49)(22,50)(23,52)(24,51)(25,45)(26,46)(27,48)(28,47)(29,65)(30,66)(31,68)(32,67)(33,73)(34,74)(35,76)(36,75)(37,69)(38,70)(39,72)(40,71); 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, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3, s4*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s4*s3*s2 >;