Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1200,1006)
Rank
5
Schläfli Type
{2,5,10,6}
Vertices, edges, …
2, 5, 25, 30, 6
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 := (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)(28,34)(29,33)(30,37)(31,36)(32,35)(38,49)(39,48)(40,52)(41,51)(42,50)(43,44)(45,47)(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 := ( 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);;
s4 := ( 3,28)( 4,29)( 5,30)( 6,31)( 7,32)( 8,33)( 9,34)(10,35)(11,36)(12,37)(13,38)(14,39)(15,40)(16,41)(17,42)(18,43)(19,44)(20,45)(21,46)(22,47)(23,48)(24,49)(25,50)(26,51)(27,52);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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)(28,34)(29,33)(30,37)(31,36)(32,35)(38,49)(39,48)(40,52)(41,51)(42,50)(43,44)(45,47)(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)!( 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);
s4 := Sym(77)!( 3,28)( 4,29)( 5,30)( 6,31)( 7,32)( 8,33)( 9,34)(10,35)(11,36)(12,37)(13,38)(14,39)(15,40)(16,41)(17,42)(18,43)(19,44)(20,45)(21,46)(22,47)(23,48)(24,49)(25,50)(26,51)(27,52);
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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;