Overview
- Group
- SmallGroup(720,813)
- Rank
- 4
- Schläfli Type
- {10,6,6}
- Vertices, edges, …
- 10, 30, 18, 6
- Order of s0s1s2s3
- 30
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
9-fold
10-fold
15-fold
18-fold
30-fold
45-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39)(42,45)(43,44)(47,50)(48,49)(52,55)(53,54)(57,60)(58,59)(62,65)(63,64)(67,70)(68,69)(72,75)(73,74)(77,80)(78,79)(82,85)(83,84)(87,90)(88,89);; s1 := ( 1, 2)( 3, 5)( 6,12)( 7,11)( 8,15)( 9,14)(10,13)(16,32)(17,31)(18,35)(19,34)(20,33)(21,42)(22,41)(23,45)(24,44)(25,43)(26,37)(27,36)(28,40)(29,39)(30,38)(46,47)(48,50)(51,57)(52,56)(53,60)(54,59)(55,58)(61,77)(62,76)(63,80)(64,79)(65,78)(66,87)(67,86)(68,90)(69,89)(70,88)(71,82)(72,81)(73,85)(74,84)(75,83);; s2 := ( 1,66)( 2,67)( 3,68)( 4,69)( 5,70)( 6,61)( 7,62)( 8,63)( 9,64)(10,65)(11,71)(12,72)(13,73)(14,74)(15,75)(16,51)(17,52)(18,53)(19,54)(20,55)(21,46)(22,47)(23,48)(24,49)(25,50)(26,56)(27,57)(28,58)(29,59)(30,60)(31,81)(32,82)(33,83)(34,84)(35,85)(36,76)(37,77)(38,78)(39,79)(40,80)(41,86)(42,87)(43,88)(44,89)(45,90);; s3 := ( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(21,26)(22,27)(23,28)(24,29)(25,30)(36,41)(37,42)(38,43)(39,44)(40,45)(51,56)(52,57)(53,58)(54,59)(55,60)(66,71)(67,72)(68,73)(69,74)(70,75)(81,86)(82,87)(83,88)(84,89)(85,90);; 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, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
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(90)!( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39)(42,45)(43,44)(47,50)(48,49)(52,55)(53,54)(57,60)(58,59)(62,65)(63,64)(67,70)(68,69)(72,75)(73,74)(77,80)(78,79)(82,85)(83,84)(87,90)(88,89); s1 := Sym(90)!( 1, 2)( 3, 5)( 6,12)( 7,11)( 8,15)( 9,14)(10,13)(16,32)(17,31)(18,35)(19,34)(20,33)(21,42)(22,41)(23,45)(24,44)(25,43)(26,37)(27,36)(28,40)(29,39)(30,38)(46,47)(48,50)(51,57)(52,56)(53,60)(54,59)(55,58)(61,77)(62,76)(63,80)(64,79)(65,78)(66,87)(67,86)(68,90)(69,89)(70,88)(71,82)(72,81)(73,85)(74,84)(75,83); s2 := Sym(90)!( 1,66)( 2,67)( 3,68)( 4,69)( 5,70)( 6,61)( 7,62)( 8,63)( 9,64)(10,65)(11,71)(12,72)(13,73)(14,74)(15,75)(16,51)(17,52)(18,53)(19,54)(20,55)(21,46)(22,47)(23,48)(24,49)(25,50)(26,56)(27,57)(28,58)(29,59)(30,60)(31,81)(32,82)(33,83)(34,84)(35,85)(36,76)(37,77)(38,78)(39,79)(40,80)(41,86)(42,87)(43,88)(44,89)(45,90); s3 := Sym(90)!( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(21,26)(22,27)(23,28)(24,29)(25,30)(36,41)(37,42)(38,43)(39,44)(40,45)(51,56)(52,57)(53,58)(54,59)(55,60)(66,71)(67,72)(68,73)(69,74)(70,75)(81,86)(82,87)(83,88)(84,89)(85,90); poly := sub<Sym(90)|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, s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.