Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1200,1028)
Rank
5
Schläfli Type
{2,2,10,15}
Vertices, edges, …
2, 2, 10, 75, 15
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 := (1,2);;
s1 := (3,4);;
s2 := (10,25)(11,26)(12,27)(13,28)(14,29)(15,20)(16,21)(17,22)(18,23)(19,24)(35,50)(36,51)(37,52)(38,53)(39,54)(40,45)(41,46)(42,47)(43,48)(44,49)(60,75)(61,76)(62,77)(63,78)(64,79)(65,70)(66,71)(67,72)(68,73)(69,74);;
s3 := ( 5,10)( 6,14)( 7,13)( 8,12)( 9,11)(15,25)(16,29)(17,28)(18,27)(19,26)(21,24)(22,23)(30,60)(31,64)(32,63)(33,62)(34,61)(35,55)(36,59)(37,58)(38,57)(39,56)(40,75)(41,79)(42,78)(43,77)(44,76)(45,70)(46,74)(47,73)(48,72)(49,71)(50,65)(51,69)(52,68)(53,67)(54,66);;
s4 := ( 5,31)( 6,30)( 7,34)( 8,33)( 9,32)(10,51)(11,50)(12,54)(13,53)(14,52)(15,46)(16,45)(17,49)(18,48)(19,47)(20,41)(21,40)(22,44)(23,43)(24,42)(25,36)(26,35)(27,39)(28,38)(29,37)(55,56)(57,59)(60,76)(61,75)(62,79)(63,78)(64,77)(65,71)(66,70)(67,74)(68,73)(69,72);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(79)!(1,2);
s1 := Sym(79)!(3,4);
s2 := Sym(79)!(10,25)(11,26)(12,27)(13,28)(14,29)(15,20)(16,21)(17,22)(18,23)(19,24)(35,50)(36,51)(37,52)(38,53)(39,54)(40,45)(41,46)(42,47)(43,48)(44,49)(60,75)(61,76)(62,77)(63,78)(64,79)(65,70)(66,71)(67,72)(68,73)(69,74);
s3 := Sym(79)!( 5,10)( 6,14)( 7,13)( 8,12)( 9,11)(15,25)(16,29)(17,28)(18,27)(19,26)(21,24)(22,23)(30,60)(31,64)(32,63)(33,62)(34,61)(35,55)(36,59)(37,58)(38,57)(39,56)(40,75)(41,79)(42,78)(43,77)(44,76)(45,70)(46,74)(47,73)(48,72)(49,71)(50,65)(51,69)(52,68)(53,67)(54,66);
s4 := Sym(79)!( 5,31)( 6,30)( 7,34)( 8,33)( 9,32)(10,51)(11,50)(12,54)(13,53)(14,52)(15,46)(16,45)(17,49)(18,48)(19,47)(20,41)(21,40)(22,44)(23,43)(24,42)(25,36)(26,35)(27,39)(28,38)(29,37)(55,56)(57,59)(60,76)(61,75)(62,79)(63,78)(64,77)(65,71)(66,70)(67,74)(68,73)(69,72);
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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;