Polytope of Type {2,2,4,14,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,14,4}*1792
if this polytope has a name.
Group : SmallGroup(1792,1076475)
Rank : 6
Schlafli Type : {2,2,4,14,4}
Number of vertices, edges, etc : 2, 2, 4, 28, 28, 4
Order of s0s1s2s3s4s5 : 28
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) :
2-fold quotients : {2,2,2,14,4}*896, {2,2,4,14,2}*896
4-fold quotients : {2,2,2,14,2}*448
7-fold quotients : {2,2,4,2,4}*256
8-fold quotients : {2,2,2,7,2}*224
14-fold quotients : {2,2,2,2,4}*128, {2,2,4,2,2}*128
28-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)( 66, 80)( 67, 81)( 68, 82)
( 69, 83)( 70, 84)( 71, 85)( 72, 86)( 73, 87)( 74, 88)( 89,103)( 90,104)
( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)( 97,111)( 98,112)
( 99,113)(100,114)(101,115)(102,116);;
s3 := ( 5, 61)( 6, 67)( 7, 66)( 8, 65)( 9, 64)( 10, 63)( 11, 62)( 12, 68)
( 13, 74)( 14, 73)( 15, 72)( 16, 71)( 17, 70)( 18, 69)( 19, 75)( 20, 81)
( 21, 80)( 22, 79)( 23, 78)( 24, 77)( 25, 76)( 26, 82)( 27, 88)( 28, 87)
( 29, 86)( 30, 85)( 31, 84)( 32, 83)( 33,103)( 34,109)( 35,108)( 36,107)
( 37,106)( 38,105)( 39,104)( 40,110)( 41,116)( 42,115)( 43,114)( 44,113)
( 45,112)( 46,111)( 47, 89)( 48, 95)( 49, 94)( 50, 93)( 51, 92)( 52, 91)
( 53, 90)( 54, 96)( 55,102)( 56,101)( 57,100)( 58, 99)( 59, 98)( 60, 97);;
s4 := ( 5, 6)( 7, 11)( 8, 10)( 12, 13)( 14, 18)( 15, 17)( 19, 20)( 21, 25)
( 22, 24)( 26, 27)( 28, 32)( 29, 31)( 33, 55)( 34, 54)( 35, 60)( 36, 59)
( 37, 58)( 38, 57)( 39, 56)( 40, 48)( 41, 47)( 42, 53)( 43, 52)( 44, 51)
( 45, 50)( 46, 49)( 61, 62)( 63, 67)( 64, 66)( 68, 69)( 70, 74)( 71, 73)
( 75, 76)( 77, 81)( 78, 80)( 82, 83)( 84, 88)( 85, 87)( 89,111)( 90,110)
( 91,116)( 92,115)( 93,114)( 94,113)( 95,112)( 96,104)( 97,103)( 98,109)
( 99,108)(100,107)(101,106)(102,105);;
s5 := ( 5, 33)( 6, 34)( 7, 35)( 8, 36)( 9, 37)( 10, 38)( 11, 39)( 12, 40)
( 13, 41)( 14, 42)( 15, 43)( 16, 44)( 17, 45)( 18, 46)( 19, 47)( 20, 48)
( 21, 49)( 22, 50)( 23, 51)( 24, 52)( 25, 53)( 26, 54)( 27, 55)( 28, 56)
( 29, 57)( 30, 58)( 31, 59)( 32, 60)( 61,103)( 62,104)( 63,105)( 64,106)
( 65,107)( 66,108)( 67,109)( 68,110)( 69,111)( 70,112)( 71,113)( 72,114)
( 73,115)( 74,116)( 75, 89)( 76, 90)( 77, 91)( 78, 92)( 79, 93)( 80, 94)
( 81, 95)( 82, 96)( 83, 97)( 84, 98)( 85, 99)( 86,100)( 87,101)( 88,102);;
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*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5,
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(116)!(1,2);
s1 := Sym(116)!(3,4);
s2 := Sym(116)!( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)( 66, 80)( 67, 81)
( 68, 82)( 69, 83)( 70, 84)( 71, 85)( 72, 86)( 73, 87)( 74, 88)( 89,103)
( 90,104)( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)( 97,111)
( 98,112)( 99,113)(100,114)(101,115)(102,116);
s3 := Sym(116)!( 5, 61)( 6, 67)( 7, 66)( 8, 65)( 9, 64)( 10, 63)( 11, 62)
( 12, 68)( 13, 74)( 14, 73)( 15, 72)( 16, 71)( 17, 70)( 18, 69)( 19, 75)
( 20, 81)( 21, 80)( 22, 79)( 23, 78)( 24, 77)( 25, 76)( 26, 82)( 27, 88)
( 28, 87)( 29, 86)( 30, 85)( 31, 84)( 32, 83)( 33,103)( 34,109)( 35,108)
( 36,107)( 37,106)( 38,105)( 39,104)( 40,110)( 41,116)( 42,115)( 43,114)
( 44,113)( 45,112)( 46,111)( 47, 89)( 48, 95)( 49, 94)( 50, 93)( 51, 92)
( 52, 91)( 53, 90)( 54, 96)( 55,102)( 56,101)( 57,100)( 58, 99)( 59, 98)
( 60, 97);
s4 := Sym(116)!( 5, 6)( 7, 11)( 8, 10)( 12, 13)( 14, 18)( 15, 17)( 19, 20)
( 21, 25)( 22, 24)( 26, 27)( 28, 32)( 29, 31)( 33, 55)( 34, 54)( 35, 60)
( 36, 59)( 37, 58)( 38, 57)( 39, 56)( 40, 48)( 41, 47)( 42, 53)( 43, 52)
( 44, 51)( 45, 50)( 46, 49)( 61, 62)( 63, 67)( 64, 66)( 68, 69)( 70, 74)
( 71, 73)( 75, 76)( 77, 81)( 78, 80)( 82, 83)( 84, 88)( 85, 87)( 89,111)
( 90,110)( 91,116)( 92,115)( 93,114)( 94,113)( 95,112)( 96,104)( 97,103)
( 98,109)( 99,108)(100,107)(101,106)(102,105);
s5 := Sym(116)!( 5, 33)( 6, 34)( 7, 35)( 8, 36)( 9, 37)( 10, 38)( 11, 39)
( 12, 40)( 13, 41)( 14, 42)( 15, 43)( 16, 44)( 17, 45)( 18, 46)( 19, 47)
( 20, 48)( 21, 49)( 22, 50)( 23, 51)( 24, 52)( 25, 53)( 26, 54)( 27, 55)
( 28, 56)( 29, 57)( 30, 58)( 31, 59)( 32, 60)( 61,103)( 62,104)( 63,105)
( 64,106)( 65,107)( 66,108)( 67,109)( 68,110)( 69,111)( 70,112)( 71,113)
( 72,114)( 73,115)( 74,116)( 75, 89)( 76, 90)( 77, 91)( 78, 92)( 79, 93)
( 80, 94)( 81, 95)( 82, 96)( 83, 97)( 84, 98)( 85, 99)( 86,100)( 87,101)
( 88,102);
poly := sub<Sym(116)|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*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s5*s4*s3*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5, 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