Polytope of Type {2,10,6,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,6,8}*1920
if this polytope has a name.
Group : SmallGroup(1920,235343)
Rank : 5
Schlafli Type : {2,10,6,8}
Number of vertices, edges, etc : 2, 10, 30, 24, 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 : {2,10,6,4}*960a
3-fold quotients : {2,10,2,8}*640
4-fold quotients : {2,10,6,2}*480
5-fold quotients : {2,2,6,8}*384
6-fold quotients : {2,5,2,8}*320, {2,10,2,4}*320
10-fold quotients : {2,2,6,4}*192a
12-fold quotients : {2,5,2,4}*160, {2,10,2,2}*160
15-fold quotients : {2,2,2,8}*128
20-fold quotients : {2,2,6,2}*96
24-fold quotients : {2,5,2,2}*80
30-fold quotients : {2,2,2,4}*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 := ( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)
( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)( 60, 61)
( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)( 80, 81)
( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)(100,101)
(104,107)(105,106)(109,112)(110,111)(114,117)(115,116)(119,122)(120,121);;
s2 := ( 3, 4)( 5, 7)( 8, 14)( 9, 13)( 10, 17)( 11, 16)( 12, 15)( 18, 19)
( 20, 22)( 23, 29)( 24, 28)( 25, 32)( 26, 31)( 27, 30)( 33, 34)( 35, 37)
( 38, 44)( 39, 43)( 40, 47)( 41, 46)( 42, 45)( 48, 49)( 50, 52)( 53, 59)
( 54, 58)( 55, 62)( 56, 61)( 57, 60)( 63, 64)( 65, 67)( 68, 74)( 69, 73)
( 70, 77)( 71, 76)( 72, 75)( 78, 79)( 80, 82)( 83, 89)( 84, 88)( 85, 92)
( 86, 91)( 87, 90)( 93, 94)( 95, 97)( 98,104)( 99,103)(100,107)(101,106)
(102,105)(108,109)(110,112)(113,119)(114,118)(115,122)(116,121)(117,120);;
s3 := ( 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);;
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,
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(122)!(1,2);
s1 := Sym(122)!( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)
( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)
( 60, 61)( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)
( 80, 81)( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)
(100,101)(104,107)(105,106)(109,112)(110,111)(114,117)(115,116)(119,122)
(120,121);
s2 := Sym(122)!( 3, 4)( 5, 7)( 8, 14)( 9, 13)( 10, 17)( 11, 16)( 12, 15)
( 18, 19)( 20, 22)( 23, 29)( 24, 28)( 25, 32)( 26, 31)( 27, 30)( 33, 34)
( 35, 37)( 38, 44)( 39, 43)( 40, 47)( 41, 46)( 42, 45)( 48, 49)( 50, 52)
( 53, 59)( 54, 58)( 55, 62)( 56, 61)( 57, 60)( 63, 64)( 65, 67)( 68, 74)
( 69, 73)( 70, 77)( 71, 76)( 72, 75)( 78, 79)( 80, 82)( 83, 89)( 84, 88)
( 85, 92)( 86, 91)( 87, 90)( 93, 94)( 95, 97)( 98,104)( 99,103)(100,107)
(101,106)(102,105)(108,109)(110,112)(113,119)(114,118)(115,122)(116,121)
(117,120);
s3 := 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);
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, 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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope