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