Overview
- Group
- SmallGroup(576,1738)
- Rank
- 4
- Schläfli Type
- {2,18,8}
- Vertices, edges, …
- 2, 18, 72, 8
- Order of s0s1s2s3
- 72
- Order of s0s1s2s3s2s1
- 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
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 6,10)( 7, 9)( 8,11)(13,14)(15,19)(16,18)(17,20)(22,23)(24,28)(25,27)(26,29)(31,32)(33,37)(34,36)(35,38)(40,41)(42,46)(43,45)(44,47)(49,50)(51,55)(52,54)(53,56)(58,59)(60,64)(61,63)(62,65)(67,68)(69,73)(70,72)(71,74);; s2 := ( 3, 6)( 4, 8)( 5, 7)( 9,10)(12,15)(13,17)(14,16)(18,19)(21,33)(22,35)(23,34)(24,30)(25,32)(26,31)(27,37)(28,36)(29,38)(39,60)(40,62)(41,61)(42,57)(43,59)(44,58)(45,64)(46,63)(47,65)(48,69)(49,71)(50,70)(51,66)(52,68)(53,67)(54,73)(55,72)(56,74);; s3 := ( 3,39)( 4,40)( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)(11,47)(12,48)(13,49)(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,66)(22,67)(23,68)(24,69)(25,70)(26,71)(27,72)(28,73)(29,74)(30,57)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(74)!(1,2); s1 := Sym(74)!( 4, 5)( 6,10)( 7, 9)( 8,11)(13,14)(15,19)(16,18)(17,20)(22,23)(24,28)(25,27)(26,29)(31,32)(33,37)(34,36)(35,38)(40,41)(42,46)(43,45)(44,47)(49,50)(51,55)(52,54)(53,56)(58,59)(60,64)(61,63)(62,65)(67,68)(69,73)(70,72)(71,74); s2 := Sym(74)!( 3, 6)( 4, 8)( 5, 7)( 9,10)(12,15)(13,17)(14,16)(18,19)(21,33)(22,35)(23,34)(24,30)(25,32)(26,31)(27,37)(28,36)(29,38)(39,60)(40,62)(41,61)(42,57)(43,59)(44,58)(45,64)(46,63)(47,65)(48,69)(49,71)(50,70)(51,66)(52,68)(53,67)(54,73)(55,72)(56,74); s3 := Sym(74)!( 3,39)( 4,40)( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)(11,47)(12,48)(13,49)(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,66)(22,67)(23,68)(24,69)(25,70)(26,71)(27,72)(28,73)(29,74)(30,57)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65); poly := sub<Sym(74)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;