Overview
- Group
- SmallGroup(1200,1006)
- Rank
- 4
- Schläfli Type
- {2,30,10}
- Vertices, edges, …
- 2, 30, 150, 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
6-fold
15-fold
25-fold
30-fold
50-fold
75-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)(28,53)(29,57)(30,56)(31,55)(32,54)(33,58)(34,62)(35,61)(36,60)(37,59)(38,63)(39,67)(40,66)(41,65)(42,64)(43,68)(44,72)(45,71)(46,70)(47,69)(48,73)(49,77)(50,76)(51,75)(52,74);; s2 := ( 3,29)( 4,28)( 5,32)( 6,31)( 7,30)( 8,49)( 9,48)(10,52)(11,51)(12,50)(13,44)(14,43)(15,47)(16,46)(17,45)(18,39)(19,38)(20,42)(21,41)(22,40)(23,34)(24,33)(25,37)(26,36)(27,35)(53,54)(55,57)(58,74)(59,73)(60,77)(61,76)(62,75)(63,69)(64,68)(65,72)(66,71)(67,70);; s3 := ( 3, 8)( 4,12)( 5,11)( 6,10)( 7, 9)(13,23)(14,27)(15,26)(16,25)(17,24)(19,22)(20,21)(28,33)(29,37)(30,36)(31,35)(32,34)(38,48)(39,52)(40,51)(41,50)(42,49)(44,47)(45,46)(53,58)(54,62)(55,61)(56,60)(57,59)(63,73)(64,77)(65,76)(66,75)(67,74)(69,72)(70,71);; 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,
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(77)!(1,2); s1 := Sym(77)!( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)(28,53)(29,57)(30,56)(31,55)(32,54)(33,58)(34,62)(35,61)(36,60)(37,59)(38,63)(39,67)(40,66)(41,65)(42,64)(43,68)(44,72)(45,71)(46,70)(47,69)(48,73)(49,77)(50,76)(51,75)(52,74); s2 := Sym(77)!( 3,29)( 4,28)( 5,32)( 6,31)( 7,30)( 8,49)( 9,48)(10,52)(11,51)(12,50)(13,44)(14,43)(15,47)(16,46)(17,45)(18,39)(19,38)(20,42)(21,41)(22,40)(23,34)(24,33)(25,37)(26,36)(27,35)(53,54)(55,57)(58,74)(59,73)(60,77)(61,76)(62,75)(63,69)(64,68)(65,72)(66,71)(67,70); s3 := Sym(77)!( 3, 8)( 4,12)( 5,11)( 6,10)( 7, 9)(13,23)(14,27)(15,26)(16,25)(17,24)(19,22)(20,21)(28,33)(29,37)(30,36)(31,35)(32,34)(38,48)(39,52)(40,51)(41,50)(42,49)(44,47)(45,46)(53,58)(54,62)(55,61)(56,60)(57,59)(63,73)(64,77)(65,76)(66,75)(67,74)(69,72)(70,71); 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, s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;