Overview
- Group
- SmallGroup(600,174)
- Rank
- 3
- Schläfli Type
- {30,10}
- Vertices, edges, …
- 30, 150, 10
- 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
- Self-Petrie
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)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(26,51)(27,55)(28,54)(29,53)(30,52)(31,56)(32,60)(33,59)(34,58)(35,57)(36,61)(37,65)(38,64)(39,63)(40,62)(41,66)(42,70)(43,69)(44,68)(45,67)(46,71)(47,75)(48,74)(49,73)(50,72);; s1 := ( 1,27)( 2,26)( 3,30)( 4,29)( 5,28)( 6,47)( 7,46)( 8,50)( 9,49)(10,48)(11,42)(12,41)(13,45)(14,44)(15,43)(16,37)(17,36)(18,40)(19,39)(20,38)(21,32)(22,31)(23,35)(24,34)(25,33)(51,52)(53,55)(56,72)(57,71)(58,75)(59,74)(60,73)(61,67)(62,66)(63,70)(64,69)(65,68);; s2 := ( 1, 6)( 2,10)( 3, 9)( 4, 8)( 5, 7)(11,21)(12,25)(13,24)(14,23)(15,22)(17,20)(18,19)(26,31)(27,35)(28,34)(29,33)(30,32)(36,46)(37,50)(38,49)(39,48)(40,47)(42,45)(43,44)(51,56)(52,60)(53,59)(54,58)(55,57)(61,71)(62,75)(63,74)(64,73)(65,72)(67,70)(68,69);; 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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(75)!( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(26,51)(27,55)(28,54)(29,53)(30,52)(31,56)(32,60)(33,59)(34,58)(35,57)(36,61)(37,65)(38,64)(39,63)(40,62)(41,66)(42,70)(43,69)(44,68)(45,67)(46,71)(47,75)(48,74)(49,73)(50,72); s1 := Sym(75)!( 1,27)( 2,26)( 3,30)( 4,29)( 5,28)( 6,47)( 7,46)( 8,50)( 9,49)(10,48)(11,42)(12,41)(13,45)(14,44)(15,43)(16,37)(17,36)(18,40)(19,39)(20,38)(21,32)(22,31)(23,35)(24,34)(25,33)(51,52)(53,55)(56,72)(57,71)(58,75)(59,74)(60,73)(61,67)(62,66)(63,70)(64,69)(65,68); s2 := Sym(75)!( 1, 6)( 2,10)( 3, 9)( 4, 8)( 5, 7)(11,21)(12,25)(13,24)(14,23)(15,22)(17,20)(18,19)(26,31)(27,35)(28,34)(29,33)(30,32)(36,46)(37,50)(38,49)(39,48)(40,47)(42,45)(43,44)(51,56)(52,60)(53,59)(54,58)(55,57)(61,71)(62,75)(63,74)(64,73)(65,72)(67,70)(68,69); 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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.