Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,10,15}

Atlas Canonical Name {3,2,10,15}*1800

Overview

Group
SmallGroup(1800,678)
Rank
5
Schläfli Type
{3,2,10,15}
Vertices, edges, …
3, 3, 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 := (2,3);;
s1 := (1,2);;
s2 := ( 9,24)(10,25)(11,26)(12,27)(13,28)(14,19)(15,20)(16,21)(17,22)(18,23)(34,49)(35,50)(36,51)(37,52)(38,53)(39,44)(40,45)(41,46)(42,47)(43,48)(59,74)(60,75)(61,76)(62,77)(63,78)(64,69)(65,70)(66,71)(67,72)(68,73);;
s3 := ( 4, 9)( 5,13)( 6,12)( 7,11)( 8,10)(14,24)(15,28)(16,27)(17,26)(18,25)(20,23)(21,22)(29,59)(30,63)(31,62)(32,61)(33,60)(34,54)(35,58)(36,57)(37,56)(38,55)(39,74)(40,78)(41,77)(42,76)(43,75)(44,69)(45,73)(46,72)(47,71)(48,70)(49,64)(50,68)(51,67)(52,66)(53,65);;
s4 := ( 4,30)( 5,29)( 6,33)( 7,32)( 8,31)( 9,50)(10,49)(11,53)(12,52)(13,51)(14,45)(15,44)(16,48)(17,47)(18,46)(19,40)(20,39)(21,43)(22,42)(23,41)(24,35)(25,34)(26,38)(27,37)(28,36)(54,55)(56,58)(59,75)(60,74)(61,78)(62,77)(63,76)(64,70)(65,69)(66,73)(67,72)(68,71);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, 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(78)!(2,3);
s1 := Sym(78)!(1,2);
s2 := Sym(78)!( 9,24)(10,25)(11,26)(12,27)(13,28)(14,19)(15,20)(16,21)(17,22)(18,23)(34,49)(35,50)(36,51)(37,52)(38,53)(39,44)(40,45)(41,46)(42,47)(43,48)(59,74)(60,75)(61,76)(62,77)(63,78)(64,69)(65,70)(66,71)(67,72)(68,73);
s3 := Sym(78)!( 4, 9)( 5,13)( 6,12)( 7,11)( 8,10)(14,24)(15,28)(16,27)(17,26)(18,25)(20,23)(21,22)(29,59)(30,63)(31,62)(32,61)(33,60)(34,54)(35,58)(36,57)(37,56)(38,55)(39,74)(40,78)(41,77)(42,76)(43,75)(44,69)(45,73)(46,72)(47,71)(48,70)(49,64)(50,68)(51,67)(52,66)(53,65);
s4 := Sym(78)!( 4,30)( 5,29)( 6,33)( 7,32)( 8,31)( 9,50)(10,49)(11,53)(12,52)(13,51)(14,45)(15,44)(16,48)(17,47)(18,46)(19,40)(20,39)(21,43)(22,42)(23,41)(24,35)(25,34)(26,38)(27,37)(28,36)(54,55)(56,58)(59,75)(60,74)(61,78)(62,77)(63,76)(64,70)(65,69)(66,73)(67,72)(68,71);
poly := sub<Sym(78)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
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 >;