Polytope of Type {10,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,24}*480
Also Known As : {10,24|2}. if this polytope has another name.
Group : SmallGroup(480,324)
Rank : 3
Schlafli Type : {10,24}
Number of vertices, edges, etc : 10, 120, 24
Order of s₀s₁s₂ : 120
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,24,2} of size 960
   {10,24,4} of size 1920
   {10,24,4} of size 1920
   {10,24,4} of size 1920
   {10,24,4} of size 1920
Vertex Figure Of :
   {2,10,24} of size 960
   {4,10,24} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,12}*240
   3-fold quotients : {10,8}*160
   4-fold quotients : {10,6}*120
   5-fold quotients : {2,24}*96
   6-fold quotients : {10,4}*80
   10-fold quotients : {2,12}*48
   12-fold quotients : {10,2}*40
   15-fold quotients : {2,8}*32
   20-fold quotients : {2,6}*24
   24-fold quotients : {5,2}*20
   30-fold quotients : {2,4}*16
   40-fold quotients : {2,3}*12
   60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,48}*960, {20,24}*960a
   3-fold covers : {10,72}*1440, {30,24}*1440a, {30,24}*1440b
   4-fold covers : {20,24}*1920a, {40,24}*1920a, {40,24}*1920b, {20,48}*1920a, {20,48}*1920b, {10,96}*1920, {20,24}*1920c
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)
( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)
( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)
(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)(118,119);;
s1 := (  1,  2)(  3,  5)(  6, 12)(  7, 11)(  8, 15)(  9, 14)( 10, 13)( 16, 17)
( 18, 20)( 21, 27)( 22, 26)( 23, 30)( 24, 29)( 25, 28)( 31, 47)( 32, 46)
( 33, 50)( 34, 49)( 35, 48)( 36, 57)( 37, 56)( 38, 60)( 39, 59)( 40, 58)
( 41, 52)( 42, 51)( 43, 55)( 44, 54)( 45, 53)( 61, 92)( 62, 91)( 63, 95)
( 64, 94)( 65, 93)( 66,102)( 67,101)( 68,105)( 69,104)( 70,103)( 71, 97)
( 72, 96)( 73,100)( 74, 99)( 75, 98)( 76,107)( 77,106)( 78,110)( 79,109)
( 80,108)( 81,117)( 82,116)( 83,120)( 84,119)( 85,118)( 86,112)( 87,111)
( 88,115)( 89,114)( 90,113);;
s2 := (  1, 66)(  2, 67)(  3, 68)(  4, 69)(  5, 70)(  6, 61)(  7, 62)(  8, 63)
(  9, 64)( 10, 65)( 11, 71)( 12, 72)( 13, 73)( 14, 74)( 15, 75)( 16, 81)
( 17, 82)( 18, 83)( 19, 84)( 20, 85)( 21, 76)( 22, 77)( 23, 78)( 24, 79)
( 25, 80)( 26, 86)( 27, 87)( 28, 88)( 29, 89)( 30, 90)( 31,111)( 32,112)
( 33,113)( 34,114)( 35,115)( 36,106)( 37,107)( 38,108)( 39,109)( 40,110)
( 41,116)( 42,117)( 43,118)( 44,119)( 45,120)( 46, 96)( 47, 97)( 48, 98)
( 49, 99)( 50,100)( 51, 91)( 52, 92)( 53, 93)( 54, 94)( 55, 95)( 56,101)
( 57,102)( 58,103)( 59,104)( 60,105);;
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, 
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(120)!(  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)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)
( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)
( 98, 99)(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)
(118,119);
s1 := Sym(120)!(  1,  2)(  3,  5)(  6, 12)(  7, 11)(  8, 15)(  9, 14)( 10, 13)
( 16, 17)( 18, 20)( 21, 27)( 22, 26)( 23, 30)( 24, 29)( 25, 28)( 31, 47)
( 32, 46)( 33, 50)( 34, 49)( 35, 48)( 36, 57)( 37, 56)( 38, 60)( 39, 59)
( 40, 58)( 41, 52)( 42, 51)( 43, 55)( 44, 54)( 45, 53)( 61, 92)( 62, 91)
( 63, 95)( 64, 94)( 65, 93)( 66,102)( 67,101)( 68,105)( 69,104)( 70,103)
( 71, 97)( 72, 96)( 73,100)( 74, 99)( 75, 98)( 76,107)( 77,106)( 78,110)
( 79,109)( 80,108)( 81,117)( 82,116)( 83,120)( 84,119)( 85,118)( 86,112)
( 87,111)( 88,115)( 89,114)( 90,113);
s2 := Sym(120)!(  1, 66)(  2, 67)(  3, 68)(  4, 69)(  5, 70)(  6, 61)(  7, 62)
(  8, 63)(  9, 64)( 10, 65)( 11, 71)( 12, 72)( 13, 73)( 14, 74)( 15, 75)
( 16, 81)( 17, 82)( 18, 83)( 19, 84)( 20, 85)( 21, 76)( 22, 77)( 23, 78)
( 24, 79)( 25, 80)( 26, 86)( 27, 87)( 28, 88)( 29, 89)( 30, 90)( 31,111)
( 32,112)( 33,113)( 34,114)( 35,115)( 36,106)( 37,107)( 38,108)( 39,109)
( 40,110)( 41,116)( 42,117)( 43,118)( 44,119)( 45,120)( 46, 96)( 47, 97)
( 48, 98)( 49, 99)( 50,100)( 51, 91)( 52, 92)( 53, 93)( 54, 94)( 55, 95)
( 56,101)( 57,102)( 58,103)( 59,104)( 60,105);
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, 
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 >;

References : None.
to this polytope