Polytope of Type {2,4,4,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4,14}*1792
if this polytope has a name.
Group : SmallGroup(1792,1036279)
Rank : 5
Schlafli Type : {2,4,4,14}
Number of vertices, edges, etc : 2, 8, 16, 56, 14
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 : {2,4,4,14}*896
4-fold quotients : {2,2,4,14}*448, {2,4,2,14}*448
7-fold quotients : {2,4,4,2}*256
8-fold quotients : {2,4,2,7}*224, {2,2,2,14}*224
14-fold quotients : {2,4,4,2}*128
16-fold quotients : {2,2,2,7}*112
28-fold quotients : {2,2,4,2}*64, {2,4,2,2}*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 := ( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 22, 29)( 23, 30)( 45, 52)
( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 50, 57)( 51, 58)( 73, 80)( 74, 81)
( 75, 82)( 76, 83)( 77, 84)( 78, 85)( 79, 86)(101,108)(102,109)(103,110)
(104,111)(105,112)(106,113)(107,114);;
s2 := ( 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);;
s3 := ( 3, 87)( 4, 93)( 5, 92)( 6, 91)( 7, 90)( 8, 89)( 9, 88)( 10, 94)
( 11,100)( 12, 99)( 13, 98)( 14, 97)( 15, 96)( 16, 95)( 17,101)( 18,107)
( 19,106)( 20,105)( 21,104)( 22,103)( 23,102)( 24,108)( 25,114)( 26,113)
( 27,112)( 28,111)( 29,110)( 30,109)( 31, 59)( 32, 65)( 33, 64)( 34, 63)
( 35, 62)( 36, 61)( 37, 60)( 38, 66)( 39, 72)( 40, 71)( 41, 70)( 42, 69)
( 43, 68)( 44, 67)( 45, 73)( 46, 79)( 47, 78)( 48, 77)( 49, 76)( 50, 75)
( 51, 74)( 52, 80)( 53, 86)( 54, 85)( 55, 84)( 56, 83)( 57, 82)( 58, 81);;
s4 := ( 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, 46)( 18, 45)
( 19, 51)( 20, 50)( 21, 49)( 22, 48)( 23, 47)( 24, 53)( 25, 52)( 26, 58)
( 27, 57)( 28, 56)( 29, 55)( 30, 54)( 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)( 73,102)( 74,101)( 75,107)( 76,106)( 77,105)( 78,104)
( 79,103)( 80,109)( 81,108)( 82,114)( 83,113)( 84,112)( 85,111)( 86,110);;
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*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(114)!(1,2);
s1 := Sym(114)!( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 22, 29)( 23, 30)
( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 50, 57)( 51, 58)( 73, 80)
( 74, 81)( 75, 82)( 76, 83)( 77, 84)( 78, 85)( 79, 86)(101,108)(102,109)
(103,110)(104,111)(105,112)(106,113)(107,114);
s2 := 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);
s3 := Sym(114)!( 3, 87)( 4, 93)( 5, 92)( 6, 91)( 7, 90)( 8, 89)( 9, 88)
( 10, 94)( 11,100)( 12, 99)( 13, 98)( 14, 97)( 15, 96)( 16, 95)( 17,101)
( 18,107)( 19,106)( 20,105)( 21,104)( 22,103)( 23,102)( 24,108)( 25,114)
( 26,113)( 27,112)( 28,111)( 29,110)( 30,109)( 31, 59)( 32, 65)( 33, 64)
( 34, 63)( 35, 62)( 36, 61)( 37, 60)( 38, 66)( 39, 72)( 40, 71)( 41, 70)
( 42, 69)( 43, 68)( 44, 67)( 45, 73)( 46, 79)( 47, 78)( 48, 77)( 49, 76)
( 50, 75)( 51, 74)( 52, 80)( 53, 86)( 54, 85)( 55, 84)( 56, 83)( 57, 82)
( 58, 81);
s4 := 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, 46)
( 18, 45)( 19, 51)( 20, 50)( 21, 49)( 22, 48)( 23, 47)( 24, 53)( 25, 52)
( 26, 58)( 27, 57)( 28, 56)( 29, 55)( 30, 54)( 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)( 73,102)( 74,101)( 75,107)( 76,106)( 77,105)
( 78,104)( 79,103)( 80,109)( 81,108)( 82,114)( 83,113)( 84,112)( 85,111)
( 86,110);
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*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope