Polytope of Type {2,10,8,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,8,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,235343)
Rank : 5
Schlafli Type : {2,10,8,6}
Number of vertices, edges, etc : 2, 10, 40, 24, 6
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 : {2,10,4,6}*960
3-fold quotients : {2,10,8,2}*640
4-fold quotients : {2,10,2,6}*480
5-fold quotients : {2,2,8,6}*384
6-fold quotients : {2,10,4,2}*320
8-fold quotients : {2,5,2,6}*240, {2,10,2,3}*240
10-fold quotients : {2,2,4,6}*192a
12-fold quotients : {2,10,2,2}*160
15-fold quotients : {2,2,8,2}*128
16-fold quotients : {2,5,2,3}*120
20-fold quotients : {2,2,2,6}*96
24-fold quotients : {2,5,2,2}*80
30-fold quotients : {2,2,4,2}*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 := ( 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, 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);;
s3 := ( 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);;
s4 := ( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 18, 23)( 19, 24)( 20, 25)
( 21, 26)( 22, 27)( 33, 38)( 34, 39)( 35, 40)( 36, 41)( 37, 42)( 48, 53)
( 49, 54)( 50, 55)( 51, 56)( 52, 57)( 63, 68)( 64, 69)( 65, 70)( 66, 71)
( 67, 72)( 78, 83)( 79, 84)( 80, 85)( 81, 86)( 82, 87)( 93, 98)( 94, 99)
( 95,100)( 96,101)( 97,102)(108,113)(109,114)(110,115)(111,116)(112,117);;
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,
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,
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, 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);
s3 := 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);
s4 := Sym(122)!( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 18, 23)( 19, 24)
( 20, 25)( 21, 26)( 22, 27)( 33, 38)( 34, 39)( 35, 40)( 36, 41)( 37, 42)
( 48, 53)( 49, 54)( 50, 55)( 51, 56)( 52, 57)( 63, 68)( 64, 69)( 65, 70)
( 66, 71)( 67, 72)( 78, 83)( 79, 84)( 80, 85)( 81, 86)( 82, 87)( 93, 98)
( 94, 99)( 95,100)( 96,101)( 97,102)(108,113)(109,114)(110,115)(111,116)
(112,117);
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, 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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope