Polytope of Type {2,6,8,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,8,10}*1920
if this polytope has a name.
Group : SmallGroup(1920,235343)
Rank : 5
Schlafli Type : {2,6,8,10}
Number of vertices, edges, etc : 2, 6, 24, 40, 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 : {2,6,4,10}*960
3-fold quotients : {2,2,8,10}*640
4-fold quotients : {2,6,2,10}*480
5-fold quotients : {2,6,8,2}*384
6-fold quotients : {2,2,4,10}*320
8-fold quotients : {2,3,2,10}*240, {2,6,2,5}*240
10-fold quotients : {2,6,4,2}*192a
12-fold quotients : {2,2,2,10}*160
15-fold quotients : {2,2,8,2}*128
16-fold quotients : {2,3,2,5}*120
20-fold quotients : {2,6,2,2}*96
24-fold quotients : {2,2,2,5}*80
30-fold quotients : {2,2,4,2}*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)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 53, 58)
( 54, 59)( 55, 60)( 56, 61)( 57, 62)( 68, 73)( 69, 74)( 70, 75)( 71, 76)
( 72, 77)( 83, 88)( 84, 89)( 85, 90)( 86, 91)( 87, 92)( 98,103)( 99,104)
(100,105)(101,106)(102,107)(113,118)(114,119)(115,120)(116,121)(117,122);;
s2 := ( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 18, 23)( 19, 24)( 20, 25)
( 21, 26)( 22, 27)( 33, 53)( 34, 54)( 35, 55)( 36, 56)( 37, 57)( 38, 48)
( 39, 49)( 40, 50)( 41, 51)( 42, 52)( 43, 58)( 44, 59)( 45, 60)( 46, 61)
( 47, 62)( 63, 98)( 64, 99)( 65,100)( 66,101)( 67,102)( 68, 93)( 69, 94)
( 70, 95)( 71, 96)( 72, 97)( 73,103)( 74,104)( 75,105)( 76,106)( 77,107)
( 78,113)( 79,114)( 80,115)( 81,116)( 82,117)( 83,108)( 84,109)( 85,110)
( 86,111)( 87,112)( 88,118)( 89,119)( 90,120)( 91,121)( 92,122);;
s3 := ( 3, 63)( 4, 67)( 5, 66)( 6, 65)( 7, 64)( 8, 68)( 9, 72)( 10, 71)
( 11, 70)( 12, 69)( 13, 73)( 14, 77)( 15, 76)( 16, 75)( 17, 74)( 18, 78)
( 19, 82)( 20, 81)( 21, 80)( 22, 79)( 23, 83)( 24, 87)( 25, 86)( 26, 85)
( 27, 84)( 28, 88)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33,108)( 34,112)
( 35,111)( 36,110)( 37,109)( 38,113)( 39,117)( 40,116)( 41,115)( 42,114)
( 43,118)( 44,122)( 45,121)( 46,120)( 47,119)( 48, 93)( 49, 97)( 50, 96)
( 51, 95)( 52, 94)( 53, 98)( 54,102)( 55,101)( 56,100)( 57, 99)( 58,103)
( 59,107)( 60,106)( 61,105)( 62,104);;
s4 := ( 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);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
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,
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(122)!(1,2);
s1 := Sym(122)!( 8, 13)( 9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)
( 25, 30)( 26, 31)( 27, 32)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)
( 53, 58)( 54, 59)( 55, 60)( 56, 61)( 57, 62)( 68, 73)( 69, 74)( 70, 75)
( 71, 76)( 72, 77)( 83, 88)( 84, 89)( 85, 90)( 86, 91)( 87, 92)( 98,103)
( 99,104)(100,105)(101,106)(102,107)(113,118)(114,119)(115,120)(116,121)
(117,122);
s2 := Sym(122)!( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 18, 23)( 19, 24)
( 20, 25)( 21, 26)( 22, 27)( 33, 53)( 34, 54)( 35, 55)( 36, 56)( 37, 57)
( 38, 48)( 39, 49)( 40, 50)( 41, 51)( 42, 52)( 43, 58)( 44, 59)( 45, 60)
( 46, 61)( 47, 62)( 63, 98)( 64, 99)( 65,100)( 66,101)( 67,102)( 68, 93)
( 69, 94)( 70, 95)( 71, 96)( 72, 97)( 73,103)( 74,104)( 75,105)( 76,106)
( 77,107)( 78,113)( 79,114)( 80,115)( 81,116)( 82,117)( 83,108)( 84,109)
( 85,110)( 86,111)( 87,112)( 88,118)( 89,119)( 90,120)( 91,121)( 92,122);
s3 := Sym(122)!( 3, 63)( 4, 67)( 5, 66)( 6, 65)( 7, 64)( 8, 68)( 9, 72)
( 10, 71)( 11, 70)( 12, 69)( 13, 73)( 14, 77)( 15, 76)( 16, 75)( 17, 74)
( 18, 78)( 19, 82)( 20, 81)( 21, 80)( 22, 79)( 23, 83)( 24, 87)( 25, 86)
( 26, 85)( 27, 84)( 28, 88)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33,108)
( 34,112)( 35,111)( 36,110)( 37,109)( 38,113)( 39,117)( 40,116)( 41,115)
( 42,114)( 43,118)( 44,122)( 45,121)( 46,120)( 47,119)( 48, 93)( 49, 97)
( 50, 96)( 51, 95)( 52, 94)( 53, 98)( 54,102)( 55,101)( 56,100)( 57, 99)
( 58,103)( 59,107)( 60,106)( 61,105)( 62,104);
s4 := Sym(122)!( 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);
poly := sub<Sym(122)|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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, 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,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope