Polytope of Type {2,14,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,4,4}*1792
if this polytope has a name.
Group : SmallGroup(1792,1036279)
Rank : 5
Schlafli Type : {2,14,4,4}
Number of vertices, edges, etc : 2, 14, 56, 16, 8
Order of s0s1s2s3s4 : 28
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 : {2,14,4,4}*896
4-fold quotients : {2,14,2,4}*448, {2,14,4,2}*448
7-fold quotients : {2,2,4,4}*256
8-fold quotients : {2,7,2,4}*224, {2,14,2,2}*224
14-fold quotients : {2,2,4,4}*128
16-fold quotients : {2,7,2,2}*112
28-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
56-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 31)( 4, 37)( 5, 36)( 6, 35)( 7, 34)( 8, 33)( 9, 32)( 10, 38)
( 11, 44)( 12, 43)( 13, 42)( 14, 41)( 15, 40)( 16, 39)( 17, 45)( 18, 51)
( 19, 50)( 20, 49)( 21, 48)( 22, 47)( 23, 46)( 24, 52)( 25, 58)( 26, 57)
( 27, 56)( 28, 55)( 29, 54)( 30, 53)( 59, 87)( 60, 93)( 61, 92)( 62, 91)
( 63, 90)( 64, 89)( 65, 88)( 66, 94)( 67,100)( 68, 99)( 69, 98)( 70, 97)
( 71, 96)( 72, 95)( 73,101)( 74,107)( 75,106)( 76,105)( 77,104)( 78,103)
( 79,102)( 80,108)( 81,114)( 82,113)( 83,112)( 84,111)( 85,110)( 86,109);;
s2 := ( 3, 32)( 4, 31)( 5, 37)( 6, 36)( 7, 35)( 8, 34)( 9, 33)( 10, 39)
( 11, 38)( 12, 44)( 13, 43)( 14, 42)( 15, 41)( 16, 40)( 17, 53)( 18, 52)
( 19, 58)( 20, 57)( 21, 56)( 22, 55)( 23, 54)( 24, 46)( 25, 45)( 26, 51)
( 27, 50)( 28, 49)( 29, 48)( 30, 47)( 59, 88)( 60, 87)( 61, 93)( 62, 92)
( 63, 91)( 64, 90)( 65, 89)( 66, 95)( 67, 94)( 68,100)( 69, 99)( 70, 98)
( 71, 97)( 72, 96)( 73,109)( 74,108)( 75,114)( 76,113)( 77,112)( 78,111)
( 79,110)( 80,102)( 81,101)( 82,107)( 83,106)( 84,105)( 85,104)( 86,103);;
s3 := ( 59, 73)( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)( 66, 80)
( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 71, 85)( 72, 86)( 87,101)( 88,102)
( 89,103)( 90,104)( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)
( 97,111)( 98,112)( 99,113)(100,114);;
s4 := ( 3, 59)( 4, 60)( 5, 61)( 6, 62)( 7, 63)( 8, 64)( 9, 65)( 10, 66)
( 11, 67)( 12, 68)( 13, 69)( 14, 70)( 15, 71)( 16, 72)( 17, 73)( 18, 74)
( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)( 24, 80)( 25, 81)( 26, 82)
( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 87)( 32, 88)( 33, 89)( 34, 90)
( 35, 91)( 36, 92)( 37, 93)( 38, 94)( 39, 95)( 40, 96)( 41, 97)( 42, 98)
( 43, 99)( 44,100)( 45,101)( 46,102)( 47,103)( 48,104)( 49,105)( 50,106)
( 51,107)( 52,108)( 53,109)( 54,110)( 55,111)( 56,112)( 57,113)( 58,114);;
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*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*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(114)!(1,2);
s1 := Sym(114)!( 3, 31)( 4, 37)( 5, 36)( 6, 35)( 7, 34)( 8, 33)( 9, 32)
( 10, 38)( 11, 44)( 12, 43)( 13, 42)( 14, 41)( 15, 40)( 16, 39)( 17, 45)
( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)( 23, 46)( 24, 52)( 25, 58)
( 26, 57)( 27, 56)( 28, 55)( 29, 54)( 30, 53)( 59, 87)( 60, 93)( 61, 92)
( 62, 91)( 63, 90)( 64, 89)( 65, 88)( 66, 94)( 67,100)( 68, 99)( 69, 98)
( 70, 97)( 71, 96)( 72, 95)( 73,101)( 74,107)( 75,106)( 76,105)( 77,104)
( 78,103)( 79,102)( 80,108)( 81,114)( 82,113)( 83,112)( 84,111)( 85,110)
( 86,109);
s2 := Sym(114)!( 3, 32)( 4, 31)( 5, 37)( 6, 36)( 7, 35)( 8, 34)( 9, 33)
( 10, 39)( 11, 38)( 12, 44)( 13, 43)( 14, 42)( 15, 41)( 16, 40)( 17, 53)
( 18, 52)( 19, 58)( 20, 57)( 21, 56)( 22, 55)( 23, 54)( 24, 46)( 25, 45)
( 26, 51)( 27, 50)( 28, 49)( 29, 48)( 30, 47)( 59, 88)( 60, 87)( 61, 93)
( 62, 92)( 63, 91)( 64, 90)( 65, 89)( 66, 95)( 67, 94)( 68,100)( 69, 99)
( 70, 98)( 71, 97)( 72, 96)( 73,109)( 74,108)( 75,114)( 76,113)( 77,112)
( 78,111)( 79,110)( 80,102)( 81,101)( 82,107)( 83,106)( 84,105)( 85,104)
( 86,103);
s3 := Sym(114)!( 59, 73)( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)
( 66, 80)( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 71, 85)( 72, 86)( 87,101)
( 88,102)( 89,103)( 90,104)( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)
( 96,110)( 97,111)( 98,112)( 99,113)(100,114);
s4 := Sym(114)!( 3, 59)( 4, 60)( 5, 61)( 6, 62)( 7, 63)( 8, 64)( 9, 65)
( 10, 66)( 11, 67)( 12, 68)( 13, 69)( 14, 70)( 15, 71)( 16, 72)( 17, 73)
( 18, 74)( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)( 24, 80)( 25, 81)
( 26, 82)( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 87)( 32, 88)( 33, 89)
( 34, 90)( 35, 91)( 36, 92)( 37, 93)( 38, 94)( 39, 95)( 40, 96)( 41, 97)
( 42, 98)( 43, 99)( 44,100)( 45,101)( 46,102)( 47,103)( 48,104)( 49,105)
( 50,106)( 51,107)( 52,108)( 53,109)( 54,110)( 55,111)( 56,112)( 57,113)
( 58,114);
poly := sub<Sym(114)|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*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope