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