Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,30,6}

Atlas Canonical Name {2,30,6}*1800

Overview

Group
SmallGroup(1800,586)
Rank
4
Schläfli Type
{2,30,6}
Vertices, edges, …
2, 75, 225, 15
Order of s0s1s2s3
6
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-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)(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 := ( 3,29)( 4,28)( 5,32)( 6,31)( 7,30)( 8,37)( 9,36)(10,35)(11,34)(12,33)(13,40)(14,39)(15,38)(16,42)(17,41)(18,43)(19,47)(20,46)(21,45)(22,44)(23,51)(24,50)(25,49)(26,48)(27,52)(53,54)(55,57)(58,62)(59,61)(63,65)(66,67)(69,72)(70,71)(73,76)(74,75);;
s3 := ( 4,26)( 5,19)( 6,17)( 7,10)( 8,16)(11,25)(12,18)(13,24)(14,22)(20,23)(29,51)(30,44)(31,42)(32,35)(33,41)(36,50)(37,43)(38,49)(39,47)(45,48)(54,76)(55,69)(56,67)(57,60)(58,66)(61,75)(62,68)(63,74)(64,72)(70,73);;
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*s1*s2*s3*s1*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s3*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)!( 3,29)( 4,28)( 5,32)( 6,31)( 7,30)( 8,37)( 9,36)(10,35)(11,34)(12,33)(13,40)(14,39)(15,38)(16,42)(17,41)(18,43)(19,47)(20,46)(21,45)(22,44)(23,51)(24,50)(25,49)(26,48)(27,52)(53,54)(55,57)(58,62)(59,61)(63,65)(66,67)(69,72)(70,71)(73,76)(74,75);
s3 := Sym(77)!( 4,26)( 5,19)( 6,17)( 7,10)( 8,16)(11,25)(12,18)(13,24)(14,22)(20,23)(29,51)(30,44)(31,42)(32,35)(33,41)(36,50)(37,43)(38,49)(39,47)(45,48)(54,76)(55,69)(56,67)(57,60)(58,66)(61,75)(62,68)(63,74)(64,72)(70,73);
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*s1*s2*s3*s1*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s3*s2 >;