Polytope of Type {4,20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,20,6}*960
Also Known As : {{4,20|2},{20,6|2}}. if this polytope has another name.
Group : SmallGroup(960,7401)
Rank : 4
Schlafli Type : {4,20,6}
Number of vertices, edges, etc : 4, 40, 60, 6
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,20,6,2} of size 1920
Vertex Figure Of :
   {2,4,20,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,20,6}*480a, {4,10,6}*480
   3-fold quotients : {4,20,2}*320
   4-fold quotients : {2,10,6}*240
   5-fold quotients : {4,4,6}*192
   6-fold quotients : {2,20,2}*160, {4,10,2}*160
   10-fold quotients : {2,4,6}*96a, {4,2,6}*96
   12-fold quotients : {2,10,2}*80
   15-fold quotients : {4,4,2}*64
   20-fold quotients : {4,2,3}*48, {2,2,6}*48
   24-fold quotients : {2,5,2}*40
   30-fold quotients : {2,4,2}*32, {4,2,2}*32
   40-fold quotients : {2,2,3}*24
   60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,20,12}*1920, {8,20,6}*1920a, {4,40,6}*1920a, {8,20,6}*1920b, {4,40,6}*1920b, {4,20,6}*1920a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope