Part of the Atlas of Small Regular Polytopes

Polytope of Type {15,10,2,2}

Atlas Canonical Name {15,10,2,2}*1200

Overview

Group
SmallGroup(1200,1028)
Rank
5
Schläfli Type
{15,10,2,2}
Vertices, edges, …
15, 75, 10, 2, 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

15-fold

25-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := ( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)(14,18)(15,17)(26,51)(27,55)(28,54)(29,53)(30,52)(31,71)(32,75)(33,74)(34,73)(35,72)(36,66)(37,70)(38,69)(39,68)(40,67)(41,61)(42,65)(43,64)(44,63)(45,62)(46,56)(47,60)(48,59)(49,58)(50,57);;
s1 := ( 1,32)( 2,31)( 3,35)( 4,34)( 5,33)( 6,27)( 7,26)( 8,30)( 9,29)(10,28)(11,47)(12,46)(13,50)(14,49)(15,48)(16,42)(17,41)(18,45)(19,44)(20,43)(21,37)(22,36)(23,40)(24,39)(25,38)(51,57)(52,56)(53,60)(54,59)(55,58)(61,72)(62,71)(63,75)(64,74)(65,73)(66,67)(68,70);;
s2 := ( 6,21)( 7,22)( 8,23)( 9,24)(10,25)(11,16)(12,17)(13,18)(14,19)(15,20)(31,46)(32,47)(33,48)(34,49)(35,50)(36,41)(37,42)(38,43)(39,44)(40,45)(56,71)(57,72)(58,73)(59,74)(60,75)(61,66)(62,67)(63,68)(64,69)(65,70);;
s3 := (76,77);;
s4 := (78,79);;
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, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(79)!( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)(14,18)(15,17)(26,51)(27,55)(28,54)(29,53)(30,52)(31,71)(32,75)(33,74)(34,73)(35,72)(36,66)(37,70)(38,69)(39,68)(40,67)(41,61)(42,65)(43,64)(44,63)(45,62)(46,56)(47,60)(48,59)(49,58)(50,57);
s1 := Sym(79)!( 1,32)( 2,31)( 3,35)( 4,34)( 5,33)( 6,27)( 7,26)( 8,30)( 9,29)(10,28)(11,47)(12,46)(13,50)(14,49)(15,48)(16,42)(17,41)(18,45)(19,44)(20,43)(21,37)(22,36)(23,40)(24,39)(25,38)(51,57)(52,56)(53,60)(54,59)(55,58)(61,72)(62,71)(63,75)(64,74)(65,73)(66,67)(68,70);
s2 := Sym(79)!( 6,21)( 7,22)( 8,23)( 9,24)(10,25)(11,16)(12,17)(13,18)(14,19)(15,20)(31,46)(32,47)(33,48)(34,49)(35,50)(36,41)(37,42)(38,43)(39,44)(40,45)(56,71)(57,72)(58,73)(59,74)(60,75)(61,66)(62,67)(63,68)(64,69)(65,70);
s3 := Sym(79)!(76,77);
s4 := Sym(79)!(78,79);
poly := sub<Sym(79)|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, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;