Polytope of Type {10,6,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,6,3,2}*960
if this polytope has a name.
Group : SmallGroup(960,11372)
Rank : 5
Schlafli Type : {10,6,3,2}
Number of vertices, edges, etc : 10, 40, 12, 4, 2
Order of s₀s₁s₂s₃s₄ : 20
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,6,3,2,2} of size 1920
Vertex Figure Of :
   {2,10,6,3,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,6,3,2}*192
   10-fold quotients : {2,3,3,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,6,3,2}*1920, {10,12,3,2}*1920, {10,6,6,2}*1920
Permutation Representation (GAP) :

s0 := (  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)( 12, 16)
( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)( 32, 36)
( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)( 52, 56)
( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)
( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)(112,116);;
s1 := (  1,  5)(  2,  7)(  3,  6)(  4,  8)(  9, 17)( 10, 19)( 11, 18)( 12, 20)
( 14, 15)( 21, 45)( 22, 47)( 23, 46)( 24, 48)( 25, 41)( 26, 43)( 27, 42)
( 28, 44)( 29, 57)( 30, 59)( 31, 58)( 32, 60)( 33, 53)( 34, 55)( 35, 54)
( 36, 56)( 37, 49)( 38, 51)( 39, 50)( 40, 52)( 61, 65)( 62, 67)( 63, 66)
( 64, 68)( 69, 77)( 70, 79)( 71, 78)( 72, 80)( 74, 75)( 81,105)( 82,107)
( 83,106)( 84,108)( 85,101)( 86,103)( 87,102)( 88,104)( 89,117)( 90,119)
( 91,118)( 92,120)( 93,113)( 94,115)( 95,114)( 96,116)( 97,109)( 98,111)
( 99,110)(100,112);;
s2 := (  1, 81)(  2, 82)(  3, 84)(  4, 83)(  5, 85)(  6, 86)(  7, 88)(  8, 87)
(  9, 89)( 10, 90)( 11, 92)( 12, 91)( 13, 93)( 14, 94)( 15, 96)( 16, 95)
( 17, 97)( 18, 98)( 19,100)( 20, 99)( 21, 61)( 22, 62)( 23, 64)( 24, 63)
( 25, 65)( 26, 66)( 27, 68)( 28, 67)( 29, 69)( 30, 70)( 31, 72)( 32, 71)
( 33, 73)( 34, 74)( 35, 76)( 36, 75)( 37, 77)( 38, 78)( 39, 80)( 40, 79)
( 41,101)( 42,102)( 43,104)( 44,103)( 45,105)( 46,106)( 47,108)( 48,107)
( 49,109)( 50,110)( 51,112)( 52,111)( 53,113)( 54,114)( 55,116)( 56,115)
( 57,117)( 58,118)( 59,120)( 60,119);;
s3 := (  1, 64)(  2, 62)(  3, 63)(  4, 61)(  5, 68)(  6, 66)(  7, 67)(  8, 65)
(  9, 72)( 10, 70)( 11, 71)( 12, 69)( 13, 76)( 14, 74)( 15, 75)( 16, 73)
( 17, 80)( 18, 78)( 19, 79)( 20, 77)( 21,104)( 22,102)( 23,103)( 24,101)
( 25,108)( 26,106)( 27,107)( 28,105)( 29,112)( 30,110)( 31,111)( 32,109)
( 33,116)( 34,114)( 35,115)( 36,113)( 37,120)( 38,118)( 39,119)( 40,117)
( 41, 84)( 42, 82)( 43, 83)( 44, 81)( 45, 88)( 46, 86)( 47, 87)( 48, 85)
( 49, 92)( 50, 90)( 51, 91)( 52, 89)( 53, 96)( 54, 94)( 55, 95)( 56, 93)
( 57,100)( 58, 98)( 59, 99)( 60, 97);;
s4 := (121,122);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(122)!(  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)
( 12, 16)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)
( 32, 36)( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)
( 52, 56)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)
( 72, 76)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)
(112,116);
s1 := Sym(122)!(  1,  5)(  2,  7)(  3,  6)(  4,  8)(  9, 17)( 10, 19)( 11, 18)
( 12, 20)( 14, 15)( 21, 45)( 22, 47)( 23, 46)( 24, 48)( 25, 41)( 26, 43)
( 27, 42)( 28, 44)( 29, 57)( 30, 59)( 31, 58)( 32, 60)( 33, 53)( 34, 55)
( 35, 54)( 36, 56)( 37, 49)( 38, 51)( 39, 50)( 40, 52)( 61, 65)( 62, 67)
( 63, 66)( 64, 68)( 69, 77)( 70, 79)( 71, 78)( 72, 80)( 74, 75)( 81,105)
( 82,107)( 83,106)( 84,108)( 85,101)( 86,103)( 87,102)( 88,104)( 89,117)
( 90,119)( 91,118)( 92,120)( 93,113)( 94,115)( 95,114)( 96,116)( 97,109)
( 98,111)( 99,110)(100,112);
s2 := Sym(122)!(  1, 81)(  2, 82)(  3, 84)(  4, 83)(  5, 85)(  6, 86)(  7, 88)
(  8, 87)(  9, 89)( 10, 90)( 11, 92)( 12, 91)( 13, 93)( 14, 94)( 15, 96)
( 16, 95)( 17, 97)( 18, 98)( 19,100)( 20, 99)( 21, 61)( 22, 62)( 23, 64)
( 24, 63)( 25, 65)( 26, 66)( 27, 68)( 28, 67)( 29, 69)( 30, 70)( 31, 72)
( 32, 71)( 33, 73)( 34, 74)( 35, 76)( 36, 75)( 37, 77)( 38, 78)( 39, 80)
( 40, 79)( 41,101)( 42,102)( 43,104)( 44,103)( 45,105)( 46,106)( 47,108)
( 48,107)( 49,109)( 50,110)( 51,112)( 52,111)( 53,113)( 54,114)( 55,116)
( 56,115)( 57,117)( 58,118)( 59,120)( 60,119);
s3 := Sym(122)!(  1, 64)(  2, 62)(  3, 63)(  4, 61)(  5, 68)(  6, 66)(  7, 67)
(  8, 65)(  9, 72)( 10, 70)( 11, 71)( 12, 69)( 13, 76)( 14, 74)( 15, 75)
( 16, 73)( 17, 80)( 18, 78)( 19, 79)( 20, 77)( 21,104)( 22,102)( 23,103)
( 24,101)( 25,108)( 26,106)( 27,107)( 28,105)( 29,112)( 30,110)( 31,111)
( 32,109)( 33,116)( 34,114)( 35,115)( 36,113)( 37,120)( 38,118)( 39,119)
( 40,117)( 41, 84)( 42, 82)( 43, 83)( 44, 81)( 45, 88)( 46, 86)( 47, 87)
( 48, 85)( 49, 92)( 50, 90)( 51, 91)( 52, 89)( 53, 96)( 54, 94)( 55, 95)
( 56, 93)( 57,100)( 58, 98)( 59, 99)( 60, 97);
s4 := Sym(122)!(121,122);
poly := sub<Sym(122)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope