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Polytope of Type {12,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,20}*480
Also Known As : {12,20|2}. if this polytope has another name.
Group : SmallGroup(480,552)
Rank : 3
Schlafli Type : {12,20}
Number of vertices, edges, etc : 12, 120, 20
Order of s0s1s2 : 60
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,20,2} of size 960
   {12,20,4} of size 1920
Vertex Figure Of :
   {2,12,20} of size 960
   {4,12,20} of size 1920
   {3,12,20} of size 1920
   {4,12,20} of size 1920
   {4,12,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,10}*240, {6,20}*240a
   3-fold quotients : {4,20}*160
   4-fold quotients : {6,10}*120
   5-fold quotients : {12,4}*96a
   6-fold quotients : {2,20}*80, {4,10}*80
   10-fold quotients : {12,2}*48, {6,4}*48a
   12-fold quotients : {2,10}*40
   15-fold quotients : {4,4}*32
   20-fold quotients : {6,2}*24
   24-fold quotients : {2,5}*20
   30-fold quotients : {2,4}*16, {4,2}*16
   40-fold quotients : {3,2}*12
   60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,20}*960a, {24,20}*960a, {12,40}*960a, {24,20}*960b, {12,40}*960b
   3-fold covers : {36,20}*1440, {12,60}*1440a, {12,60}*1440b
   4-fold covers : {12,40}*1920a, {24,20}*1920a, {24,40}*1920a, {24,40}*1920b, {24,40}*1920c, {24,40}*1920d, {12,80}*1920a, {48,20}*1920a, {12,80}*1920b, {48,20}*1920b, {12,40}*1920b, {24,20}*1920b, {12,20}*1920a, {12,20}*1920c
Permutation Representation (GAP) :
s0 := (  6, 11)(  7, 12)(  8, 13)(  9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)
( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 56)
( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 61, 76)( 62, 77)( 63, 78)( 64, 79)
( 65, 80)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)( 71, 81)( 72, 82)
( 73, 83)( 74, 84)( 75, 85)( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)
( 96,116)( 97,117)( 98,118)( 99,119)(100,120)(101,111)(102,112)(103,113)
(104,114)(105,115);;
s1 := (  1, 66)(  2, 70)(  3, 69)(  4, 68)(  5, 67)(  6, 61)(  7, 65)(  8, 64)
(  9, 63)( 10, 62)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 81)
( 17, 85)( 18, 84)( 19, 83)( 20, 82)( 21, 76)( 22, 80)( 23, 79)( 24, 78)
( 25, 77)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 96)( 32,100)
( 33, 99)( 34, 98)( 35, 97)( 36, 91)( 37, 95)( 38, 94)( 39, 93)( 40, 92)
( 41,101)( 42,105)( 43,104)( 44,103)( 45,102)( 46,111)( 47,115)( 48,114)
( 49,113)( 50,112)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)( 56,116)
( 57,120)( 58,119)( 59,118)( 60,117);;
s2 := (  1,  2)(  3,  5)(  6,  7)(  8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)
( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)
( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)
( 61, 92)( 62, 91)( 63, 95)( 64, 94)( 65, 93)( 66, 97)( 67, 96)( 68,100)
( 69, 99)( 70, 98)( 71,102)( 72,101)( 73,105)( 74,104)( 75,103)( 76,107)
( 77,106)( 78,110)( 79,109)( 80,108)( 81,112)( 82,111)( 83,115)( 84,114)
( 85,113)( 86,117)( 87,116)( 88,120)( 89,119)( 90,118);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*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, 
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)!(  6, 11)(  7, 12)(  8, 13)(  9, 14)( 10, 15)( 21, 26)( 22, 27)
( 23, 28)( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)
( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 61, 76)( 62, 77)( 63, 78)
( 64, 79)( 65, 80)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)( 71, 81)
( 72, 82)( 73, 83)( 74, 84)( 75, 85)( 91,106)( 92,107)( 93,108)( 94,109)
( 95,110)( 96,116)( 97,117)( 98,118)( 99,119)(100,120)(101,111)(102,112)
(103,113)(104,114)(105,115);
s1 := Sym(120)!(  1, 66)(  2, 70)(  3, 69)(  4, 68)(  5, 67)(  6, 61)(  7, 65)
(  8, 64)(  9, 63)( 10, 62)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)
( 16, 81)( 17, 85)( 18, 84)( 19, 83)( 20, 82)( 21, 76)( 22, 80)( 23, 79)
( 24, 78)( 25, 77)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 96)
( 32,100)( 33, 99)( 34, 98)( 35, 97)( 36, 91)( 37, 95)( 38, 94)( 39, 93)
( 40, 92)( 41,101)( 42,105)( 43,104)( 44,103)( 45,102)( 46,111)( 47,115)
( 48,114)( 49,113)( 50,112)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)
( 56,116)( 57,120)( 58,119)( 59,118)( 60,117);
s2 := Sym(120)!(  1,  2)(  3,  5)(  6,  7)(  8, 10)( 11, 12)( 13, 15)( 16, 17)
( 18, 20)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)
( 38, 40)( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)
( 58, 60)( 61, 92)( 62, 91)( 63, 95)( 64, 94)( 65, 93)( 66, 97)( 67, 96)
( 68,100)( 69, 99)( 70, 98)( 71,102)( 72,101)( 73,105)( 74,104)( 75,103)
( 76,107)( 77,106)( 78,110)( 79,109)( 80,108)( 81,112)( 82,111)( 83,115)
( 84,114)( 85,113)( 86,117)( 87,116)( 88,120)( 89,119)( 90,118);
poly := sub<Sym(120)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*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, 
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.
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