Polytope of Type {2,8,28}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,28}*896a
if this polytope has a name.
Group : SmallGroup(896,10954)
Rank : 4
Schlafli Type : {2,8,28}
Number of vertices, edges, etc : 2, 8, 112, 28
Order of s0s1s2s3 : 56
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,8,28,2} of size 1792
Vertex Figure Of :
{2,2,8,28} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4,28}*448, {2,8,14}*448
4-fold quotients : {2,2,28}*224, {2,4,14}*224
7-fold quotients : {2,8,4}*128a
8-fold quotients : {2,2,14}*112
14-fold quotients : {2,4,4}*64, {2,8,2}*64
16-fold quotients : {2,2,7}*56
28-fold quotients : {2,2,4}*32, {2,4,2}*32
56-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,8,28}*1792a, {2,8,56}*1792a, {2,8,56}*1792c, {4,8,28}*1792d, {2,16,28}*1792a, {2,16,28}*1792b
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)( 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);;
s2 := ( 3, 59)( 4, 65)( 5, 64)( 6, 63)( 7, 62)( 8, 61)( 9, 60)( 10, 66)
( 11, 72)( 12, 71)( 13, 70)( 14, 69)( 15, 68)( 16, 67)( 17, 80)( 18, 86)
( 19, 85)( 20, 84)( 21, 83)( 22, 82)( 23, 81)( 24, 73)( 25, 79)( 26, 78)
( 27, 77)( 28, 76)( 29, 75)( 30, 74)( 31, 87)( 32, 93)( 33, 92)( 34, 91)
( 35, 90)( 36, 89)( 37, 88)( 38, 94)( 39,100)( 40, 99)( 41, 98)( 42, 97)
( 43, 96)( 44, 95)( 45,108)( 46,114)( 47,113)( 48,112)( 49,111)( 50,110)
( 51,109)( 52,101)( 53,107)( 54,106)( 55,105)( 56,104)( 57,103)( 58,102);;
s3 := ( 3, 4)( 5, 9)( 6, 8)( 10, 11)( 12, 16)( 13, 15)( 17, 18)( 19, 23)
( 20, 22)( 24, 25)( 26, 30)( 27, 29)( 31, 32)( 33, 37)( 34, 36)( 38, 39)
( 40, 44)( 41, 43)( 45, 46)( 47, 51)( 48, 50)( 52, 53)( 54, 58)( 55, 57)
( 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]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)( 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);
s2 := Sym(114)!( 3, 59)( 4, 65)( 5, 64)( 6, 63)( 7, 62)( 8, 61)( 9, 60)
( 10, 66)( 11, 72)( 12, 71)( 13, 70)( 14, 69)( 15, 68)( 16, 67)( 17, 80)
( 18, 86)( 19, 85)( 20, 84)( 21, 83)( 22, 82)( 23, 81)( 24, 73)( 25, 79)
( 26, 78)( 27, 77)( 28, 76)( 29, 75)( 30, 74)( 31, 87)( 32, 93)( 33, 92)
( 34, 91)( 35, 90)( 36, 89)( 37, 88)( 38, 94)( 39,100)( 40, 99)( 41, 98)
( 42, 97)( 43, 96)( 44, 95)( 45,108)( 46,114)( 47,113)( 48,112)( 49,111)
( 50,110)( 51,109)( 52,101)( 53,107)( 54,106)( 55,105)( 56,104)( 57,103)
( 58,102);
s3 := Sym(114)!( 3, 4)( 5, 9)( 6, 8)( 10, 11)( 12, 16)( 13, 15)( 17, 18)
( 19, 23)( 20, 22)( 24, 25)( 26, 30)( 27, 29)( 31, 32)( 33, 37)( 34, 36)
( 38, 39)( 40, 44)( 41, 43)( 45, 46)( 47, 51)( 48, 50)( 52, 53)( 54, 58)
( 55, 57)( 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>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope