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