Overview
- Group
- SmallGroup(1200,1006)
- Rank
- 4
- Schläfli Type
- {2,10,30}
- Vertices, edges, …
- 2, 10, 150, 30
- 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)( 8,23)( 9,27)(10,26)(11,25)(12,24)(13,18)(14,22)(15,21)(16,20)(17,19)(29,32)(30,31)(33,48)(34,52)(35,51)(36,50)(37,49)(38,43)(39,47)(40,46)(41,45)(42,44)(54,57)(55,56)(58,73)(59,77)(60,76)(61,75)(62,74)(63,68)(64,72)(65,71)(66,70)(67,69);; s2 := ( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,24)(14,23)(15,27)(16,26)(17,25)(18,19)(20,22)(28,59)(29,58)(30,62)(31,61)(32,60)(33,54)(34,53)(35,57)(36,56)(37,55)(38,74)(39,73)(40,77)(41,76)(42,75)(43,69)(44,68)(45,72)(46,71)(47,70)(48,64)(49,63)(50,67)(51,66)(52,65);; s3 := ( 3,28)( 4,32)( 5,31)( 6,30)( 7,29)( 8,33)( 9,37)(10,36)(11,35)(12,34)(13,38)(14,42)(15,41)(16,40)(17,39)(18,43)(19,47)(20,46)(21,45)(22,44)(23,48)(24,52)(25,51)(26,50)(27,49)(54,57)(55,56)(59,62)(60,61)(64,67)(65,66)(69,72)(70,71)(74,77)(75,76);; 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*s3*s2*s3*s2*s3*s2*s3*s2*s3*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 ];;
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)(29,32)(30,31)(33,48)(34,52)(35,51)(36,50)(37,49)(38,43)(39,47)(40,46)(41,45)(42,44)(54,57)(55,56)(58,73)(59,77)(60,76)(61,75)(62,74)(63,68)(64,72)(65,71)(66,70)(67,69); s2 := Sym(77)!( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,24)(14,23)(15,27)(16,26)(17,25)(18,19)(20,22)(28,59)(29,58)(30,62)(31,61)(32,60)(33,54)(34,53)(35,57)(36,56)(37,55)(38,74)(39,73)(40,77)(41,76)(42,75)(43,69)(44,68)(45,72)(46,71)(47,70)(48,64)(49,63)(50,67)(51,66)(52,65); s3 := Sym(77)!( 3,28)( 4,32)( 5,31)( 6,30)( 7,29)( 8,33)( 9,37)(10,36)(11,35)(12,34)(13,38)(14,42)(15,41)(16,40)(17,39)(18,43)(19,47)(20,46)(21,45)(22,44)(23,48)(24,52)(25,51)(26,50)(27,49)(54,57)(55,56)(59,62)(60,61)(64,67)(65,66)(69,72)(70,71)(74,77)(75,76); 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*s3*s2*s3*s2*s3*s2*s3*s2*s3*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 >;