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