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