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