Overview
- Group
- SmallGroup(600,195)
- Rank
- 4
- Schläfli Type
- {2,15,10}
- Vertices, edges, …
- 2, 15, 75, 10
- Order of s0s1s2s3
- 30
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
15-fold
25-fold
Covers minimal covers in bold
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 7)( 5, 6)( 8,23)( 9,27)(10,26)(11,25)(12,24)(13,18)(14,22)(15,21)(16,20)(17,19)(28,53)(29,57)(30,56)(31,55)(32,54)(33,73)(34,77)(35,76)(36,75)(37,74)(38,68)(39,72)(40,71)(41,70)(42,69)(43,63)(44,67)(45,66)(46,65)(47,64)(48,58)(49,62)(50,61)(51,60)(52,59);; s2 := ( 3,34)( 4,33)( 5,37)( 6,36)( 7,35)( 8,29)( 9,28)(10,32)(11,31)(12,30)(13,49)(14,48)(15,52)(16,51)(17,50)(18,44)(19,43)(20,47)(21,46)(22,45)(23,39)(24,38)(25,42)(26,41)(27,40)(53,59)(54,58)(55,62)(56,61)(57,60)(63,74)(64,73)(65,77)(66,76)(67,75)(68,69)(70,72);; s3 := ( 8,23)( 9,24)(10,25)(11,26)(12,27)(13,18)(14,19)(15,20)(16,21)(17,22)(33,48)(34,49)(35,50)(36,51)(37,52)(38,43)(39,44)(40,45)(41,46)(42,47)(58,73)(59,74)(60,75)(61,76)(62,77)(63,68)(64,69)(65,70)(66,71)(67,72);; 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,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(77)!(1,2); s1 := Sym(77)!( 4, 7)( 5, 6)( 8,23)( 9,27)(10,26)(11,25)(12,24)(13,18)(14,22)(15,21)(16,20)(17,19)(28,53)(29,57)(30,56)(31,55)(32,54)(33,73)(34,77)(35,76)(36,75)(37,74)(38,68)(39,72)(40,71)(41,70)(42,69)(43,63)(44,67)(45,66)(46,65)(47,64)(48,58)(49,62)(50,61)(51,60)(52,59); s2 := Sym(77)!( 3,34)( 4,33)( 5,37)( 6,36)( 7,35)( 8,29)( 9,28)(10,32)(11,31)(12,30)(13,49)(14,48)(15,52)(16,51)(17,50)(18,44)(19,43)(20,47)(21,46)(22,45)(23,39)(24,38)(25,42)(26,41)(27,40)(53,59)(54,58)(55,62)(56,61)(57,60)(63,74)(64,73)(65,77)(66,76)(67,75)(68,69)(70,72); s3 := Sym(77)!( 8,23)( 9,24)(10,25)(11,26)(12,27)(13,18)(14,19)(15,20)(16,21)(17,22)(33,48)(34,49)(35,50)(36,51)(37,52)(38,43)(39,44)(40,45)(41,46)(42,47)(58,73)(59,74)(60,75)(61,76)(62,77)(63,68)(64,69)(65,70)(66,71)(67,72); poly := sub<Sym(77)|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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;