Part of the Atlas of Small Regular Polytopes

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

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

Overview

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