Overview
- Group
- SmallGroup(600,174)
- Rank
- 3
- Schläfli Type
- {10,30}
- Vertices, edges, …
- 10, 150, 30
- Order of s0s1s2
- 30
- Order of s0s1s2s1
- 10
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
6-fold
15-fold
25-fold
30-fold
50-fold
75-fold
Covers minimal covers in bold
2-fold
3-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)(14,18)(15,17)(27,30)(28,29)(31,46)(32,50)(33,49)(34,48)(35,47)(36,41)(37,45)(38,44)(39,43)(40,42)(52,55)(53,54)(56,71)(57,75)(58,74)(59,73)(60,72)(61,66)(62,70)(63,69)(64,68)(65,67);; s1 := ( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,22)(12,21)(13,25)(14,24)(15,23)(16,17)(18,20)(26,57)(27,56)(28,60)(29,59)(30,58)(31,52)(32,51)(33,55)(34,54)(35,53)(36,72)(37,71)(38,75)(39,74)(40,73)(41,67)(42,66)(43,70)(44,69)(45,68)(46,62)(47,61)(48,65)(49,64)(50,63);; s2 := ( 1,26)( 2,30)( 3,29)( 4,28)( 5,27)( 6,31)( 7,35)( 8,34)( 9,33)(10,32)(11,36)(12,40)(13,39)(14,38)(15,37)(16,41)(17,45)(18,44)(19,43)(20,42)(21,46)(22,50)(23,49)(24,48)(25,47)(52,55)(53,54)(57,60)(58,59)(62,65)(63,64)(67,70)(68,69)(72,75)(73,74);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*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(75)!( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)(14,18)(15,17)(27,30)(28,29)(31,46)(32,50)(33,49)(34,48)(35,47)(36,41)(37,45)(38,44)(39,43)(40,42)(52,55)(53,54)(56,71)(57,75)(58,74)(59,73)(60,72)(61,66)(62,70)(63,69)(64,68)(65,67); s1 := Sym(75)!( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,22)(12,21)(13,25)(14,24)(15,23)(16,17)(18,20)(26,57)(27,56)(28,60)(29,59)(30,58)(31,52)(32,51)(33,55)(34,54)(35,53)(36,72)(37,71)(38,75)(39,74)(40,73)(41,67)(42,66)(43,70)(44,69)(45,68)(46,62)(47,61)(48,65)(49,64)(50,63); s2 := Sym(75)!( 1,26)( 2,30)( 3,29)( 4,28)( 5,27)( 6,31)( 7,35)( 8,34)( 9,33)(10,32)(11,36)(12,40)(13,39)(14,38)(15,37)(16,41)(17,45)(18,44)(19,43)(20,42)(21,46)(22,50)(23,49)(24,48)(25,47)(52,55)(53,54)(57,60)(58,59)(62,65)(63,64)(67,70)(68,69)(72,75)(73,74); poly := sub<Sym(75)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1, 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.