Overview
- Group
- SmallGroup(1152,153178)
- Rank
- 6
- Schläfli Type
- {2,2,2,12,6}
- Vertices, edges, …
- 2, 2, 2, 12, 36, 6
- Order of s0s1s2s3s4s5
- 12
- Order of s0s1s2s3s4s5s4s3s2s1
- 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
9-fold
12-fold
18-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := (5,6);; s3 := ( 7,43)( 8,45)( 9,44)(10,49)(11,51)(12,50)(13,46)(14,48)(15,47)(16,52)(17,54)(18,53)(19,58)(20,60)(21,59)(22,55)(23,57)(24,56)(25,70)(26,72)(27,71)(28,76)(29,78)(30,77)(31,73)(32,75)(33,74)(34,61)(35,63)(36,62)(37,67)(38,69)(39,68)(40,64)(41,66)(42,65);; s4 := ( 7,65)( 8,64)( 9,66)(10,62)(11,61)(12,63)(13,68)(14,67)(15,69)(16,74)(17,73)(18,75)(19,71)(20,70)(21,72)(22,77)(23,76)(24,78)(25,47)(26,46)(27,48)(28,44)(29,43)(30,45)(31,50)(32,49)(33,51)(34,56)(35,55)(36,57)(37,53)(38,52)(39,54)(40,59)(41,58)(42,60);; s5 := ( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72)(74,75)(77,78);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4,
s3*s4*s3*s4*s5*s4*s3*s4*s3*s4*s5*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(78)!(1,2); s1 := Sym(78)!(3,4); s2 := Sym(78)!(5,6); s3 := Sym(78)!( 7,43)( 8,45)( 9,44)(10,49)(11,51)(12,50)(13,46)(14,48)(15,47)(16,52)(17,54)(18,53)(19,58)(20,60)(21,59)(22,55)(23,57)(24,56)(25,70)(26,72)(27,71)(28,76)(29,78)(30,77)(31,73)(32,75)(33,74)(34,61)(35,63)(36,62)(37,67)(38,69)(39,68)(40,64)(41,66)(42,65); s4 := Sym(78)!( 7,65)( 8,64)( 9,66)(10,62)(11,61)(12,63)(13,68)(14,67)(15,69)(16,74)(17,73)(18,75)(19,71)(20,70)(21,72)(22,77)(23,76)(24,78)(25,47)(26,46)(27,48)(28,44)(29,43)(30,45)(31,50)(32,49)(33,51)(34,56)(35,55)(36,57)(37,53)(38,52)(39,54)(40,59)(41,58)(42,60); s5 := Sym(78)!( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72)(74,75)(77,78); poly := sub<Sym(78)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, s3*s4*s3*s4*s5*s4*s3*s4*s3*s4*s5*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;