Polytope of Type {20,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,12,2}*960
if this polytope has a name.
Group : SmallGroup(960,8838)
Rank : 4
Schlafli Type : {20,12,2}
Number of vertices, edges, etc : 20, 120, 12, 2
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {20,12,2,2} of size 1920
Vertex Figure Of :
   {2,20,12,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,12,2}*480, {20,6,2}*480a
   3-fold quotients : {20,4,2}*320
   4-fold quotients : {10,6,2}*240
   5-fold quotients : {4,12,2}*192a
   6-fold quotients : {20,2,2}*160, {10,4,2}*160
   10-fold quotients : {2,12,2}*96, {4,6,2}*96a
   12-fold quotients : {10,2,2}*80
   15-fold quotients : {4,4,2}*64
   20-fold quotients : {2,6,2}*48
   24-fold quotients : {5,2,2}*40
   30-fold quotients : {2,4,2}*32, {4,2,2}*32
   40-fold quotients : {2,3,2}*24
   60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,12,4}*1920a, {40,12,2}*1920a, {20,24,2}*1920a, {40,12,2}*1920b, {20,24,2}*1920b, {20,12,2}*1920a
Permutation Representation (GAP) :

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

to this polytope