Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,3,10}

Atlas Canonical Name {6,3,10}*1800

Overview

Group
SmallGroup(1800,575)
Rank
4
Schläfli Type
{6,3,10}
Vertices, edges, …
6, 45, 75, 50
Order of s0s1s2s3
6
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

25-fold

75-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s1*(s2*s1*s3)^2*s2> of order 5

10 facets

6 vertex figures

P/N, where N=<s1*s2*s1*(s3*s2)^2*s1*s3*s2*s1*s3> of order 5

10 facets

6 vertex figures

Representations

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

References

None.

to this polytope.