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Polytope of Type {2,2,6,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,20}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 5
Schlafli Type : {2,2,6,20}
Number of vertices, edges, etc : 2, 2, 12, 120, 40
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,6,20}*960b
   4-fold quotients : {2,2,6,10}*480
   5-fold quotients : {2,2,6,4}*384
   10-fold quotients : {2,2,3,4}*192, {2,2,6,4}*192b, {2,2,6,4}*192c
   12-fold quotients : {2,2,2,10}*160
   20-fold quotients : {2,2,3,4}*96, {2,2,6,2}*96
   24-fold quotients : {2,2,2,5}*80
   40-fold quotients : {2,2,3,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (  6,  7)( 10, 11)( 14, 15)( 18, 19)( 22, 23)( 25, 45)( 26, 47)( 27, 46)
( 28, 48)( 29, 49)( 30, 51)( 31, 50)( 32, 52)( 33, 53)( 34, 55)( 35, 54)
( 36, 56)( 37, 57)( 38, 59)( 39, 58)( 40, 60)( 41, 61)( 42, 63)( 43, 62)
( 44, 64)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 82, 83)( 85,105)( 86,107)
( 87,106)( 88,108)( 89,109)( 90,111)( 91,110)( 92,112)( 93,113)( 94,115)
( 95,114)( 96,116)( 97,117)( 98,119)( 99,118)(100,120)(101,121)(102,123)
(103,122)(104,124);;
s3 := (  5, 25)(  6, 26)(  7, 28)(  8, 27)(  9, 41)( 10, 42)( 11, 44)( 12, 43)
( 13, 37)( 14, 38)( 15, 40)( 16, 39)( 17, 33)( 18, 34)( 19, 36)( 20, 35)
( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 47, 48)( 49, 61)( 50, 62)( 51, 64)
( 52, 63)( 53, 57)( 54, 58)( 55, 60)( 56, 59)( 65, 85)( 66, 86)( 67, 88)
( 68, 87)( 69,101)( 70,102)( 71,104)( 72,103)( 73, 97)( 74, 98)( 75,100)
( 76, 99)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 81, 89)( 82, 90)( 83, 92)
( 84, 91)(107,108)(109,121)(110,122)(111,124)(112,123)(113,117)(114,118)
(115,120)(116,119);;
s4 := (  5, 72)(  6, 71)(  7, 70)(  8, 69)(  9, 68)( 10, 67)( 11, 66)( 12, 65)
( 13, 84)( 14, 83)( 15, 82)( 16, 81)( 17, 80)( 18, 79)( 19, 78)( 20, 77)
( 21, 76)( 22, 75)( 23, 74)( 24, 73)( 25, 92)( 26, 91)( 27, 90)( 28, 89)
( 29, 88)( 30, 87)( 31, 86)( 32, 85)( 33,104)( 34,103)( 35,102)( 36,101)
( 37,100)( 38, 99)( 39, 98)( 40, 97)( 41, 96)( 42, 95)( 43, 94)( 44, 93)
( 45,112)( 46,111)( 47,110)( 48,109)( 49,108)( 50,107)( 51,106)( 52,105)
( 53,124)( 54,123)( 55,122)( 56,121)( 57,120)( 58,119)( 59,118)( 60,117)
( 61,116)( 62,115)( 63,114)( 64,113);;
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*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3, 
s4*s2*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(124)!(1,2);
s1 := Sym(124)!(3,4);
s2 := Sym(124)!(  6,  7)( 10, 11)( 14, 15)( 18, 19)( 22, 23)( 25, 45)( 26, 47)
( 27, 46)( 28, 48)( 29, 49)( 30, 51)( 31, 50)( 32, 52)( 33, 53)( 34, 55)
( 35, 54)( 36, 56)( 37, 57)( 38, 59)( 39, 58)( 40, 60)( 41, 61)( 42, 63)
( 43, 62)( 44, 64)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 82, 83)( 85,105)
( 86,107)( 87,106)( 88,108)( 89,109)( 90,111)( 91,110)( 92,112)( 93,113)
( 94,115)( 95,114)( 96,116)( 97,117)( 98,119)( 99,118)(100,120)(101,121)
(102,123)(103,122)(104,124);
s3 := Sym(124)!(  5, 25)(  6, 26)(  7, 28)(  8, 27)(  9, 41)( 10, 42)( 11, 44)
( 12, 43)( 13, 37)( 14, 38)( 15, 40)( 16, 39)( 17, 33)( 18, 34)( 19, 36)
( 20, 35)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 47, 48)( 49, 61)( 50, 62)
( 51, 64)( 52, 63)( 53, 57)( 54, 58)( 55, 60)( 56, 59)( 65, 85)( 66, 86)
( 67, 88)( 68, 87)( 69,101)( 70,102)( 71,104)( 72,103)( 73, 97)( 74, 98)
( 75,100)( 76, 99)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 81, 89)( 82, 90)
( 83, 92)( 84, 91)(107,108)(109,121)(110,122)(111,124)(112,123)(113,117)
(114,118)(115,120)(116,119);
s4 := Sym(124)!(  5, 72)(  6, 71)(  7, 70)(  8, 69)(  9, 68)( 10, 67)( 11, 66)
( 12, 65)( 13, 84)( 14, 83)( 15, 82)( 16, 81)( 17, 80)( 18, 79)( 19, 78)
( 20, 77)( 21, 76)( 22, 75)( 23, 74)( 24, 73)( 25, 92)( 26, 91)( 27, 90)
( 28, 89)( 29, 88)( 30, 87)( 31, 86)( 32, 85)( 33,104)( 34,103)( 35,102)
( 36,101)( 37,100)( 38, 99)( 39, 98)( 40, 97)( 41, 96)( 42, 95)( 43, 94)
( 44, 93)( 45,112)( 46,111)( 47,110)( 48,109)( 49,108)( 50,107)( 51,106)
( 52,105)( 53,124)( 54,123)( 55,122)( 56,121)( 57,120)( 58,119)( 59,118)
( 60,117)( 61,116)( 62,115)( 63,114)( 64,113);
poly := sub<Sym(124)|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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3, 
s4*s2*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3 >; 
 

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