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

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

Permutation Representation (Magma) :

s0 := Sym(124)!(1,2);
s1 := Sym(124)!(  8, 13)(  9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)
( 25, 30)( 26, 31)( 27, 32)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)
( 38, 58)( 39, 59)( 40, 60)( 41, 61)( 42, 62)( 43, 53)( 44, 54)( 45, 55)
( 46, 56)( 47, 57)( 63, 93)( 64, 94)( 65, 95)( 66, 96)( 67, 97)( 68,103)
( 69,104)( 70,105)( 71,106)( 72,107)( 73, 98)( 74, 99)( 75,100)( 76,101)
( 77,102)( 78,108)( 79,109)( 80,110)( 81,111)( 82,112)( 83,118)( 84,119)
( 85,120)( 86,121)( 87,122)( 88,113)( 89,114)( 90,115)( 91,116)( 92,117);
s2 := Sym(124)!(  3, 68)(  4, 72)(  5, 71)(  6, 70)(  7, 69)(  8, 63)(  9, 67)
( 10, 66)( 11, 65)( 12, 64)( 13, 73)( 14, 77)( 15, 76)( 16, 75)( 17, 74)
( 18, 83)( 19, 87)( 20, 86)( 21, 85)( 22, 84)( 23, 78)( 24, 82)( 25, 81)
( 26, 80)( 27, 79)( 28, 88)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33,113)
( 34,117)( 35,116)( 36,115)( 37,114)( 38,108)( 39,112)( 40,111)( 41,110)
( 42,109)( 43,118)( 44,122)( 45,121)( 46,120)( 47,119)( 48, 98)( 49,102)
( 50,101)( 51,100)( 52, 99)( 53, 93)( 54, 97)( 55, 96)( 56, 95)( 57, 94)
( 58,103)( 59,107)( 60,106)( 61,105)( 62,104);
s3 := Sym(124)!(  3,  4)(  5,  7)(  8,  9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)
( 20, 22)( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)
( 40, 42)( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)
( 60, 62)( 63, 64)( 65, 67)( 68, 69)( 70, 72)( 73, 74)( 75, 77)( 78, 79)
( 80, 82)( 83, 84)( 85, 87)( 88, 89)( 90, 92)( 93, 94)( 95, 97)( 98, 99)
(100,102)(103,104)(105,107)(108,109)(110,112)(113,114)(115,117)(118,119)
(120,122);
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, s2*s3*s2*s3*s2*s3*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope