Overview
- Group
- SmallGroup(1152,157448)
- Rank
- 6
- Schläfli Type
- {4,9,2,2,2}
- Vertices, edges, …
- 8, 36, 18, 2, 2, 2
- Order of s0s1s2s3s4s5
- 18
- 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
12-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 1,38)( 2,37)( 3,40)( 4,39)( 5,42)( 6,41)( 7,44)( 8,43)( 9,46)(10,45)(11,48)(12,47)(13,50)(14,49)(15,52)(16,51)(17,54)(18,53)(19,56)(20,55)(21,58)(22,57)(23,60)(24,59)(25,62)(26,61)(27,64)(28,63)(29,66)(30,65)(31,68)(32,67)(33,70)(34,69)(35,72)(36,71);; s1 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(13,29)(14,31)(15,30)(16,32)(17,25)(18,27)(19,26)(20,28)(21,33)(22,35)(23,34)(24,36)(38,39)(41,45)(42,47)(43,46)(44,48)(49,65)(50,67)(51,66)(52,68)(53,61)(54,63)(55,62)(56,64)(57,69)(58,71)(59,70)(60,72);; s2 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)(10,18)(11,20)(12,19)(25,29)(26,30)(27,32)(28,31)(35,36)(37,49)(38,50)(39,52)(40,51)(41,57)(42,58)(43,60)(44,59)(45,53)(46,54)(47,56)(48,55)(61,65)(62,66)(63,68)(64,67)(71,72);; 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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
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)!( 1,38)( 2,37)( 3,40)( 4,39)( 5,42)( 6,41)( 7,44)( 8,43)( 9,46)(10,45)(11,48)(12,47)(13,50)(14,49)(15,52)(16,51)(17,54)(18,53)(19,56)(20,55)(21,58)(22,57)(23,60)(24,59)(25,62)(26,61)(27,64)(28,63)(29,66)(30,65)(31,68)(32,67)(33,70)(34,69)(35,72)(36,71); s1 := Sym(78)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(13,29)(14,31)(15,30)(16,32)(17,25)(18,27)(19,26)(20,28)(21,33)(22,35)(23,34)(24,36)(38,39)(41,45)(42,47)(43,46)(44,48)(49,65)(50,67)(51,66)(52,68)(53,61)(54,63)(55,62)(56,64)(57,69)(58,71)(59,70)(60,72); s2 := Sym(78)!( 1,13)( 2,14)( 3,16)( 4,15)( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)(10,18)(11,20)(12,19)(25,29)(26,30)(27,32)(28,31)(35,36)(37,49)(38,50)(39,52)(40,51)(41,57)(42,58)(43,60)(44,59)(45,53)(46,54)(47,56)(48,55)(61,65)(62,66)(63,68)(64,67)(71,72); 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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;