Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,10,5,2}

Atlas Canonical Name {6,10,5,2}*1200

Overview

Group
SmallGroup(1200,1006)
Rank
5
Schläfli Type
{6,10,5,2}
Vertices, edges, …
6, 30, 25, 5, 2
Order of s0s1s2s3s4
30
Order of s0s1s2s3s4s3s2s1
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

10-fold

15-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (26,51)(27,52)(28,53)(29,54)(30,55)(31,56)(32,57)(33,58)(34,59)(35,60)(36,61)(37,62)(38,63)(39,64)(40,65)(41,66)(42,67)(43,68)(44,69)(45,70)(46,71)(47,72)(48,73)(49,74)(50,75);;
s1 := ( 1,26)( 2,30)( 3,29)( 4,28)( 5,27)( 6,31)( 7,35)( 8,34)( 9,33)(10,32)(11,36)(12,40)(13,39)(14,38)(15,37)(16,41)(17,45)(18,44)(19,43)(20,42)(21,46)(22,50)(23,49)(24,48)(25,47)(52,55)(53,54)(57,60)(58,59)(62,65)(63,64)(67,70)(68,69)(72,75)(73,74);;
s2 := ( 1, 2)( 3, 5)( 6,22)( 7,21)( 8,25)( 9,24)(10,23)(11,17)(12,16)(13,20)(14,19)(15,18)(26,27)(28,30)(31,47)(32,46)(33,50)(34,49)(35,48)(36,42)(37,41)(38,45)(39,44)(40,43)(51,52)(53,55)(56,72)(57,71)(58,75)(59,74)(60,73)(61,67)(62,66)(63,70)(64,69)(65,68);;
s3 := ( 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);;
s4 := (76,77);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(77)!(26,51)(27,52)(28,53)(29,54)(30,55)(31,56)(32,57)(33,58)(34,59)(35,60)(36,61)(37,62)(38,63)(39,64)(40,65)(41,66)(42,67)(43,68)(44,69)(45,70)(46,71)(47,72)(48,73)(49,74)(50,75);
s1 := Sym(77)!( 1,26)( 2,30)( 3,29)( 4,28)( 5,27)( 6,31)( 7,35)( 8,34)( 9,33)(10,32)(11,36)(12,40)(13,39)(14,38)(15,37)(16,41)(17,45)(18,44)(19,43)(20,42)(21,46)(22,50)(23,49)(24,48)(25,47)(52,55)(53,54)(57,60)(58,59)(62,65)(63,64)(67,70)(68,69)(72,75)(73,74);
s2 := Sym(77)!( 1, 2)( 3, 5)( 6,22)( 7,21)( 8,25)( 9,24)(10,23)(11,17)(12,16)(13,20)(14,19)(15,18)(26,27)(28,30)(31,47)(32,46)(33,50)(34,49)(35,48)(36,42)(37,41)(38,45)(39,44)(40,43)(51,52)(53,55)(56,72)(57,71)(58,75)(59,74)(60,73)(61,67)(62,66)(63,70)(64,69)(65,68);
s3 := Sym(77)!( 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);
s4 := Sym(77)!(76,77);
poly := sub<Sym(77)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;