Overview
- Group
- SmallGroup(1152,99277)
- Rank
- 4
- Schläfli Type
- {12,4,2}
- Vertices, edges, …
- 72, 144, 24, 2
- Order of s0s1s2s3
- 4
- 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
4-fold
8-fold
9-fold
18-fold
36-fold
72-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 1,46)( 2,48)( 3,47)( 4,52)( 5,54)( 6,53)( 7,49)( 8,51)( 9,50)(10,37)(11,39)(12,38)(13,43)(14,45)(15,44)(16,40)(17,42)(18,41)(19,64)(20,66)(21,65)(22,70)(23,72)(24,71)(25,67)(26,69)(27,68)(28,55)(29,57)(30,56)(31,61)(32,63)(33,62)(34,58)(35,60)(36,59);; s1 := ( 1, 5)( 3, 8)( 6, 7)(10,14)(12,17)(15,16)(19,23)(21,26)(24,25)(28,32)(30,35)(33,34)(37,68)(38,65)(39,71)(40,67)(41,64)(42,70)(43,69)(44,66)(45,72)(46,59)(47,56)(48,62)(49,58)(50,55)(51,61)(52,60)(53,57)(54,63);; s2 := ( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(19,28)(20,29)(21,30)(22,34)(23,35)(24,36)(25,31)(26,32)(27,33)(40,43)(41,44)(42,45)(49,52)(50,53)(51,54)(55,64)(56,65)(57,66)(58,70)(59,71)(60,72)(61,67)(62,68)(63,69);; 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,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(74)!( 1,46)( 2,48)( 3,47)( 4,52)( 5,54)( 6,53)( 7,49)( 8,51)( 9,50)(10,37)(11,39)(12,38)(13,43)(14,45)(15,44)(16,40)(17,42)(18,41)(19,64)(20,66)(21,65)(22,70)(23,72)(24,71)(25,67)(26,69)(27,68)(28,55)(29,57)(30,56)(31,61)(32,63)(33,62)(34,58)(35,60)(36,59); s1 := Sym(74)!( 1, 5)( 3, 8)( 6, 7)(10,14)(12,17)(15,16)(19,23)(21,26)(24,25)(28,32)(30,35)(33,34)(37,68)(38,65)(39,71)(40,67)(41,64)(42,70)(43,69)(44,66)(45,72)(46,59)(47,56)(48,62)(49,58)(50,55)(51,61)(52,60)(53,57)(54,63); s2 := Sym(74)!( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(19,28)(20,29)(21,30)(22,34)(23,35)(24,36)(25,31)(26,32)(27,33)(40,43)(41,44)(42,45)(49,52)(50,53)(51,54)(55,64)(56,65)(57,66)(58,70)(59,71)(60,72)(61,67)(62,68)(63,69); 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, s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*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 >;