Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,10,15}

Atlas Canonical Name {2,10,15}*600

Overview

Group
SmallGroup(600,195)
Rank
4
Schläfli Type
{2,10,15}
Vertices, edges, …
2, 10, 75, 15
Order of s0s1s2s3
30
Order of s0s1s2s3s2s1
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

2-fold

3-fold

Representations

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