Overview
- Group
- SmallGroup(1152,134272)
- Rank
- 5
- Schläfli Type
- {2,12,12,2}
- Vertices, edges, …
- 2, 12, 72, 12, 2
- Order of s0s1s2s3s4
- 12
- 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
9-fold
12-fold
18-fold
24-fold
36-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)(34,37)(35,38)(39,57)(40,58)(41,59)(42,63)(43,64)(44,65)(45,60)(46,61)(47,62)(48,66)(49,67)(50,68)(51,72)(52,73)(53,74)(54,69)(55,70)(56,71);; s2 := ( 3,42)( 4,44)( 5,43)( 6,39)( 7,41)( 8,40)( 9,45)(10,47)(11,46)(12,51)(13,53)(14,52)(15,48)(16,50)(17,49)(18,54)(19,56)(20,55)(21,60)(22,62)(23,61)(24,57)(25,59)(26,58)(27,63)(28,65)(29,64)(30,69)(31,71)(32,70)(33,66)(34,68)(35,67)(36,72)(37,74)(38,73);; s3 := ( 3, 4)( 6,10)( 7, 9)( 8,11)(12,13)(15,19)(16,18)(17,20)(21,22)(24,28)(25,27)(26,29)(30,31)(33,37)(34,36)(35,38)(39,67)(40,66)(41,68)(42,73)(43,72)(44,74)(45,70)(46,69)(47,71)(48,58)(49,57)(50,59)(51,64)(52,63)(53,65)(54,61)(55,60)(56,62);; 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*s3*s1*s2*s1*s2*s3*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,
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)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)(34,37)(35,38)(39,57)(40,58)(41,59)(42,63)(43,64)(44,65)(45,60)(46,61)(47,62)(48,66)(49,67)(50,68)(51,72)(52,73)(53,74)(54,69)(55,70)(56,71); s2 := Sym(76)!( 3,42)( 4,44)( 5,43)( 6,39)( 7,41)( 8,40)( 9,45)(10,47)(11,46)(12,51)(13,53)(14,52)(15,48)(16,50)(17,49)(18,54)(19,56)(20,55)(21,60)(22,62)(23,61)(24,57)(25,59)(26,58)(27,63)(28,65)(29,64)(30,69)(31,71)(32,70)(33,66)(34,68)(35,67)(36,72)(37,74)(38,73); s3 := Sym(76)!( 3, 4)( 6,10)( 7, 9)( 8,11)(12,13)(15,19)(16,18)(17,20)(21,22)(24,28)(25,27)(26,29)(30,31)(33,37)(34,36)(35,38)(39,67)(40,66)(41,68)(42,73)(43,72)(44,74)(45,70)(46,69)(47,71)(48,58)(49,57)(50,59)(51,64)(52,63)(53,65)(54,61)(55,60)(56,62); 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*s3*s1*s2*s1*s2*s3*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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;