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