Polytope of Type {2,10,4,3,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,4,3,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 6
Schlafli Type : {2,10,4,3,2}
Number of vertices, edges, etc : 2, 10, 40, 12, 6, 2
Order of s0s1s2s3s4s5 : 30
Order of s0s1s2s3s4s5s4s3s2s1 : 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) :
4-fold quotients : {2,10,2,3,2}*480
5-fold quotients : {2,2,4,3,2}*384
8-fold quotients : {2,5,2,3,2}*240
10-fold quotients : {2,2,4,3,2}*192
20-fold quotients : {2,2,2,3,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 7, 19)( 8, 20)( 9, 21)( 10, 22)( 11, 15)( 12, 16)( 13, 17)( 14, 18)
( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 35)( 32, 36)( 33, 37)( 34, 38)
( 47, 59)( 48, 60)( 49, 61)( 50, 62)( 51, 55)( 52, 56)( 53, 57)( 54, 58)
( 67, 79)( 68, 80)( 69, 81)( 70, 82)( 71, 75)( 72, 76)( 73, 77)( 74, 78)
( 87, 99)( 88,100)( 89,101)( 90,102)( 91, 95)( 92, 96)( 93, 97)( 94, 98)
(107,119)(108,120)(109,121)(110,122)(111,115)(112,116)(113,117)(114,118);;
s2 := ( 3, 69)( 4, 70)( 5, 67)( 6, 68)( 7, 65)( 8, 66)( 9, 63)( 10, 64)
( 11, 81)( 12, 82)( 13, 79)( 14, 80)( 15, 77)( 16, 78)( 17, 75)( 18, 76)
( 19, 73)( 20, 74)( 21, 71)( 22, 72)( 23, 89)( 24, 90)( 25, 87)( 26, 88)
( 27, 85)( 28, 86)( 29, 83)( 30, 84)( 31,101)( 32,102)( 33, 99)( 34,100)
( 35, 97)( 36, 98)( 37, 95)( 38, 96)( 39, 93)( 40, 94)( 41, 91)( 42, 92)
( 43,109)( 44,110)( 45,107)( 46,108)( 47,105)( 48,106)( 49,103)( 50,104)
( 51,121)( 52,122)( 53,119)( 54,120)( 55,117)( 56,118)( 57,115)( 58,116)
( 59,113)( 60,114)( 61,111)( 62,112);;
s3 := ( 4, 5)( 8, 9)( 12, 13)( 16, 17)( 20, 21)( 23, 43)( 24, 45)( 25, 44)
( 26, 46)( 27, 47)( 28, 49)( 29, 48)( 30, 50)( 31, 51)( 32, 53)( 33, 52)
( 34, 54)( 35, 55)( 36, 57)( 37, 56)( 38, 58)( 39, 59)( 40, 61)( 41, 60)
( 42, 62)( 64, 65)( 68, 69)( 72, 73)( 76, 77)( 80, 81)( 83,103)( 84,105)
( 85,104)( 86,106)( 87,107)( 88,109)( 89,108)( 90,110)( 91,111)( 92,113)
( 93,112)( 94,114)( 95,115)( 96,117)( 97,116)( 98,118)( 99,119)(100,121)
(101,120)(102,122);;
s4 := ( 3, 43)( 4, 46)( 5, 45)( 6, 44)( 7, 47)( 8, 50)( 9, 49)( 10, 48)
( 11, 51)( 12, 54)( 13, 53)( 14, 52)( 15, 55)( 16, 58)( 17, 57)( 18, 56)
( 19, 59)( 20, 62)( 21, 61)( 22, 60)( 24, 26)( 28, 30)( 32, 34)( 36, 38)
( 40, 42)( 63,103)( 64,106)( 65,105)( 66,104)( 67,107)( 68,110)( 69,109)
( 70,108)( 71,111)( 72,114)( 73,113)( 74,112)( 75,115)( 76,118)( 77,117)
( 78,116)( 79,119)( 80,122)( 81,121)( 82,120)( 84, 86)( 88, 90)( 92, 94)
( 96, 98)(100,102);;
s5 := (123,124);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5,
s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
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(124)!(1,2);
s1 := Sym(124)!( 7, 19)( 8, 20)( 9, 21)( 10, 22)( 11, 15)( 12, 16)( 13, 17)
( 14, 18)( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 35)( 32, 36)( 33, 37)
( 34, 38)( 47, 59)( 48, 60)( 49, 61)( 50, 62)( 51, 55)( 52, 56)( 53, 57)
( 54, 58)( 67, 79)( 68, 80)( 69, 81)( 70, 82)( 71, 75)( 72, 76)( 73, 77)
( 74, 78)( 87, 99)( 88,100)( 89,101)( 90,102)( 91, 95)( 92, 96)( 93, 97)
( 94, 98)(107,119)(108,120)(109,121)(110,122)(111,115)(112,116)(113,117)
(114,118);
s2 := Sym(124)!( 3, 69)( 4, 70)( 5, 67)( 6, 68)( 7, 65)( 8, 66)( 9, 63)
( 10, 64)( 11, 81)( 12, 82)( 13, 79)( 14, 80)( 15, 77)( 16, 78)( 17, 75)
( 18, 76)( 19, 73)( 20, 74)( 21, 71)( 22, 72)( 23, 89)( 24, 90)( 25, 87)
( 26, 88)( 27, 85)( 28, 86)( 29, 83)( 30, 84)( 31,101)( 32,102)( 33, 99)
( 34,100)( 35, 97)( 36, 98)( 37, 95)( 38, 96)( 39, 93)( 40, 94)( 41, 91)
( 42, 92)( 43,109)( 44,110)( 45,107)( 46,108)( 47,105)( 48,106)( 49,103)
( 50,104)( 51,121)( 52,122)( 53,119)( 54,120)( 55,117)( 56,118)( 57,115)
( 58,116)( 59,113)( 60,114)( 61,111)( 62,112);
s3 := Sym(124)!( 4, 5)( 8, 9)( 12, 13)( 16, 17)( 20, 21)( 23, 43)( 24, 45)
( 25, 44)( 26, 46)( 27, 47)( 28, 49)( 29, 48)( 30, 50)( 31, 51)( 32, 53)
( 33, 52)( 34, 54)( 35, 55)( 36, 57)( 37, 56)( 38, 58)( 39, 59)( 40, 61)
( 41, 60)( 42, 62)( 64, 65)( 68, 69)( 72, 73)( 76, 77)( 80, 81)( 83,103)
( 84,105)( 85,104)( 86,106)( 87,107)( 88,109)( 89,108)( 90,110)( 91,111)
( 92,113)( 93,112)( 94,114)( 95,115)( 96,117)( 97,116)( 98,118)( 99,119)
(100,121)(101,120)(102,122);
s4 := Sym(124)!( 3, 43)( 4, 46)( 5, 45)( 6, 44)( 7, 47)( 8, 50)( 9, 49)
( 10, 48)( 11, 51)( 12, 54)( 13, 53)( 14, 52)( 15, 55)( 16, 58)( 17, 57)
( 18, 56)( 19, 59)( 20, 62)( 21, 61)( 22, 60)( 24, 26)( 28, 30)( 32, 34)
( 36, 38)( 40, 42)( 63,103)( 64,106)( 65,105)( 66,104)( 67,107)( 68,110)
( 69,109)( 70,108)( 71,111)( 72,114)( 73,113)( 74,112)( 75,115)( 76,118)
( 77,117)( 78,116)( 79,119)( 80,122)( 81,121)( 82,120)( 84, 86)( 88, 90)
( 92, 94)( 96, 98)(100,102);
s5 := Sym(124)!(123,124);
poly := sub<Sym(124)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
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