Overview
- Group
- SmallGroup(1152,153178)
- Rank
- 6
- Schläfli Type
- {2,2,2,6,12}
- Vertices, edges, …
- 2, 2, 2, 6, 36, 12
- 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 := ( 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);; s4 := ( 7,44)( 8,43)( 9,45)(10,50)(11,49)(12,51)(13,47)(14,46)(15,48)(16,53)(17,52)(18,54)(19,59)(20,58)(21,60)(22,56)(23,55)(24,57)(25,71)(26,70)(27,72)(28,77)(29,76)(30,78)(31,74)(32,73)(33,75)(34,62)(35,61)(36,63)(37,68)(38,67)(39,69)(40,65)(41,64)(42,66);; s5 := ( 7,64)( 8,66)( 9,65)(10,61)(11,63)(12,62)(13,67)(14,69)(15,68)(16,73)(17,75)(18,74)(19,70)(20,72)(21,71)(22,76)(23,78)(24,77)(25,46)(26,48)(27,47)(28,43)(29,45)(30,44)(31,49)(32,51)(33,50)(34,55)(35,57)(36,56)(37,52)(38,54)(39,53)(40,58)(41,60)(42,59);; 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, s3*s4*s5*s3*s4*s3*s4*s5*s3*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(78)!(1,2); s1 := Sym(78)!(3,4); s2 := Sym(78)!(5,6); s3 := 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); s4 := Sym(78)!( 7,44)( 8,43)( 9,45)(10,50)(11,49)(12,51)(13,47)(14,46)(15,48)(16,53)(17,52)(18,54)(19,59)(20,58)(21,60)(22,56)(23,55)(24,57)(25,71)(26,70)(27,72)(28,77)(29,76)(30,78)(31,74)(32,73)(33,75)(34,62)(35,61)(36,63)(37,68)(38,67)(39,69)(40,65)(41,64)(42,66); s5 := Sym(78)!( 7,64)( 8,66)( 9,65)(10,61)(11,63)(12,62)(13,67)(14,69)(15,68)(16,73)(17,75)(18,74)(19,70)(20,72)(21,71)(22,76)(23,78)(24,77)(25,46)(26,48)(27,47)(28,43)(29,45)(30,44)(31,49)(32,51)(33,50)(34,55)(35,57)(36,56)(37,52)(38,54)(39,53)(40,58)(41,60)(42,59); 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, s3*s4*s5*s3*s4*s3*s4*s5*s3*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;