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Polytope of Type {2,10,24,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,24,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,235347)
Rank : 5
Schlafli Type : {2,10,24,2}
Number of vertices, edges, etc : 2, 10, 120, 24, 2
Order of s0s1s2s3s4 : 120
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 : {2,10,12,2}*960
   3-fold quotients : {2,10,8,2}*640
   4-fold quotients : {2,10,6,2}*480
   5-fold quotients : {2,2,24,2}*384
   6-fold quotients : {2,10,4,2}*320
   10-fold quotients : {2,2,12,2}*192
   12-fold quotients : {2,10,2,2}*160
   15-fold quotients : {2,2,8,2}*128
   20-fold quotients : {2,2,6,2}*96
   24-fold quotients : {2,5,2,2}*80
   30-fold quotients : {2,2,4,2}*64
   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 := (  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)
( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)( 60, 61)
( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)( 80, 81)
( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)(100,101)
(104,107)(105,106)(109,112)(110,111)(114,117)(115,116)(119,122)(120,121);;
s2 := (  3,  4)(  5,  7)(  8, 14)(  9, 13)( 10, 17)( 11, 16)( 12, 15)( 18, 19)
( 20, 22)( 23, 29)( 24, 28)( 25, 32)( 26, 31)( 27, 30)( 33, 49)( 34, 48)
( 35, 52)( 36, 51)( 37, 50)( 38, 59)( 39, 58)( 40, 62)( 41, 61)( 42, 60)
( 43, 54)( 44, 53)( 45, 57)( 46, 56)( 47, 55)( 63, 94)( 64, 93)( 65, 97)
( 66, 96)( 67, 95)( 68,104)( 69,103)( 70,107)( 71,106)( 72,105)( 73, 99)
( 74, 98)( 75,102)( 76,101)( 77,100)( 78,109)( 79,108)( 80,112)( 81,111)
( 82,110)( 83,119)( 84,118)( 85,122)( 86,121)( 87,120)( 88,114)( 89,113)
( 90,117)( 91,116)( 92,115);;
s3 := (  3, 68)(  4, 69)(  5, 70)(  6, 71)(  7, 72)(  8, 63)(  9, 64)( 10, 65)
( 11, 66)( 12, 67)( 13, 73)( 14, 74)( 15, 75)( 16, 76)( 17, 77)( 18, 83)
( 19, 84)( 20, 85)( 21, 86)( 22, 87)( 23, 78)( 24, 79)( 25, 80)( 26, 81)
( 27, 82)( 28, 88)( 29, 89)( 30, 90)( 31, 91)( 32, 92)( 33,113)( 34,114)
( 35,115)( 36,116)( 37,117)( 38,108)( 39,109)( 40,110)( 41,111)( 42,112)
( 43,118)( 44,119)( 45,120)( 46,121)( 47,122)( 48, 98)( 49, 99)( 50,100)
( 51,101)( 52,102)( 53, 93)( 54, 94)( 55, 95)( 56, 96)( 57, 97)( 58,103)
( 59,104)( 60,105)( 61,106)( 62,107);;
s4 := (123,124);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(124)!(1,2);
s1 := Sym(124)!(  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)
( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)
( 60, 61)( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)
( 80, 81)( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)
(100,101)(104,107)(105,106)(109,112)(110,111)(114,117)(115,116)(119,122)
(120,121);
s2 := Sym(124)!(  3,  4)(  5,  7)(  8, 14)(  9, 13)( 10, 17)( 11, 16)( 12, 15)
( 18, 19)( 20, 22)( 23, 29)( 24, 28)( 25, 32)( 26, 31)( 27, 30)( 33, 49)
( 34, 48)( 35, 52)( 36, 51)( 37, 50)( 38, 59)( 39, 58)( 40, 62)( 41, 61)
( 42, 60)( 43, 54)( 44, 53)( 45, 57)( 46, 56)( 47, 55)( 63, 94)( 64, 93)
( 65, 97)( 66, 96)( 67, 95)( 68,104)( 69,103)( 70,107)( 71,106)( 72,105)
( 73, 99)( 74, 98)( 75,102)( 76,101)( 77,100)( 78,109)( 79,108)( 80,112)
( 81,111)( 82,110)( 83,119)( 84,118)( 85,122)( 86,121)( 87,120)( 88,114)
( 89,113)( 90,117)( 91,116)( 92,115);
s3 := Sym(124)!(  3, 68)(  4, 69)(  5, 70)(  6, 71)(  7, 72)(  8, 63)(  9, 64)
( 10, 65)( 11, 66)( 12, 67)( 13, 73)( 14, 74)( 15, 75)( 16, 76)( 17, 77)
( 18, 83)( 19, 84)( 20, 85)( 21, 86)( 22, 87)( 23, 78)( 24, 79)( 25, 80)
( 26, 81)( 27, 82)( 28, 88)( 29, 89)( 30, 90)( 31, 91)( 32, 92)( 33,113)
( 34,114)( 35,115)( 36,116)( 37,117)( 38,108)( 39,109)( 40,110)( 41,111)
( 42,112)( 43,118)( 44,119)( 45,120)( 46,121)( 47,122)( 48, 98)( 49, 99)
( 50,100)( 51,101)( 52,102)( 53, 93)( 54, 94)( 55, 95)( 56, 96)( 57, 97)
( 58,103)( 59,104)( 60,105)( 61,106)( 62,107);
s4 := Sym(124)!(123,124);
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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