Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,3,8}

Atlas Canonical Name {4,3,8}*768a

Overview

Group
SmallGroup(768,1090071)
Rank
4
Schläfli Type
{4,3,8}
Vertices, edges, …
4, 24, 48, 32
Order of s0s1s2s3
6
Order of s0s1s2s3s2s1
2
Also known as
{{4,3}3,{3,8}6}. if this polytope has another name.

Special Properties

  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

4-fold

8-fold

16-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*s2)^3*s1*s3*s2> of order 2

16 facets

4 vertex figures

  • 4 of 2-fold non-regular quotient of {3,8}*192
P/N, where N=<(s1*(s3*s2)^2)^2*s3> of order 2

16 facets

4 vertex figures

  • 4 of 2-fold non-regular quotient of {3,8}*192
P/N, where N=<s1*s2*s3*s2*s1*(s3*s2)^2, (s1*(s3*s2)^2)^2*s3> of order 4

8 facets

4 vertex figures

  • 4 of 4-fold non-regular quotient of {3,8}*192
P/N, where N=<s1*s2*s3*s2*s1*(s3*s2)^2*s3> of order 4

8 facets

4 vertex figures

  • 4 of 4-fold non-regular quotient of {3,8}*192
P/N, where N=<s1*(s2*s1*s3)^2*s2> of order 4

8 facets

4 vertex figures

  • 4 of 4-fold non-regular quotient of {3,8}*192

Representations

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

References

None.

to this polytope.