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