Polytope of Type {2,28,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,28,10}*1120
if this polytope has a name.
Group : SmallGroup(1120,989)
Rank : 4
Schlafli Type : {2,28,10}
Number of vertices, edges, etc : 2, 28, 140, 10
Order of s₀s₁s₂s₃ : 140
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,14,10}*560
   5-fold quotients : {2,28,2}*224
   7-fold quotients : {2,4,10}*160
   10-fold quotients : {2,14,2}*112
   14-fold quotients : {2,2,10}*80
   20-fold quotients : {2,7,2}*56
   28-fold quotients : {2,2,5}*40
   35-fold quotients : {2,4,2}*32
   70-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)( 19, 22)
( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)( 39, 44)
( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)( 55, 56)
( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 73,108)( 74,114)
( 75,113)( 76,112)( 77,111)( 78,110)( 79,109)( 80,115)( 81,121)( 82,120)
( 83,119)( 84,118)( 85,117)( 86,116)( 87,122)( 88,128)( 89,127)( 90,126)
( 91,125)( 92,124)( 93,123)( 94,129)( 95,135)( 96,134)( 97,133)( 98,132)
( 99,131)(100,130)(101,136)(102,142)(103,141)(104,140)(105,139)(106,138)
(107,137);;
s2 := (  3, 74)(  4, 73)(  5, 79)(  6, 78)(  7, 77)(  8, 76)(  9, 75)( 10,102)
( 11,101)( 12,107)( 13,106)( 14,105)( 15,104)( 16,103)( 17, 95)( 18, 94)
( 19,100)( 20, 99)( 21, 98)( 22, 97)( 23, 96)( 24, 88)( 25, 87)( 26, 93)
( 27, 92)( 28, 91)( 29, 90)( 30, 89)( 31, 81)( 32, 80)( 33, 86)( 34, 85)
( 35, 84)( 36, 83)( 37, 82)( 38,109)( 39,108)( 40,114)( 41,113)( 42,112)
( 43,111)( 44,110)( 45,137)( 46,136)( 47,142)( 48,141)( 49,140)( 50,139)
( 51,138)( 52,130)( 53,129)( 54,135)( 55,134)( 56,133)( 57,132)( 58,131)
( 59,123)( 60,122)( 61,128)( 62,127)( 63,126)( 64,125)( 65,124)( 66,116)
( 67,115)( 68,121)( 69,120)( 70,119)( 71,118)( 72,117);;
s3 := (  3, 10)(  4, 11)(  5, 12)(  6, 13)(  7, 14)(  8, 15)(  9, 16)( 17, 31)
( 18, 32)( 19, 33)( 20, 34)( 21, 35)( 22, 36)( 23, 37)( 38, 45)( 39, 46)
( 40, 47)( 41, 48)( 42, 49)( 43, 50)( 44, 51)( 52, 66)( 53, 67)( 54, 68)
( 55, 69)( 56, 70)( 57, 71)( 58, 72)( 73, 80)( 74, 81)( 75, 82)( 76, 83)
( 77, 84)( 78, 85)( 79, 86)( 87,101)( 88,102)( 89,103)( 90,104)( 91,105)
( 92,106)( 93,107)(108,115)(109,116)(110,117)(111,118)(112,119)(113,120)
(114,121)(122,136)(123,137)(124,138)(125,139)(126,140)(127,141)(128,142);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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*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(142)!(1,2);
s1 := Sym(142)!(  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)
( 19, 22)( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)
( 39, 44)( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)
( 55, 56)( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 73,108)
( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)( 79,109)( 80,115)( 81,121)
( 82,120)( 83,119)( 84,118)( 85,117)( 86,116)( 87,122)( 88,128)( 89,127)
( 90,126)( 91,125)( 92,124)( 93,123)( 94,129)( 95,135)( 96,134)( 97,133)
( 98,132)( 99,131)(100,130)(101,136)(102,142)(103,141)(104,140)(105,139)
(106,138)(107,137);
s2 := Sym(142)!(  3, 74)(  4, 73)(  5, 79)(  6, 78)(  7, 77)(  8, 76)(  9, 75)
( 10,102)( 11,101)( 12,107)( 13,106)( 14,105)( 15,104)( 16,103)( 17, 95)
( 18, 94)( 19,100)( 20, 99)( 21, 98)( 22, 97)( 23, 96)( 24, 88)( 25, 87)
( 26, 93)( 27, 92)( 28, 91)( 29, 90)( 30, 89)( 31, 81)( 32, 80)( 33, 86)
( 34, 85)( 35, 84)( 36, 83)( 37, 82)( 38,109)( 39,108)( 40,114)( 41,113)
( 42,112)( 43,111)( 44,110)( 45,137)( 46,136)( 47,142)( 48,141)( 49,140)
( 50,139)( 51,138)( 52,130)( 53,129)( 54,135)( 55,134)( 56,133)( 57,132)
( 58,131)( 59,123)( 60,122)( 61,128)( 62,127)( 63,126)( 64,125)( 65,124)
( 66,116)( 67,115)( 68,121)( 69,120)( 70,119)( 71,118)( 72,117);
s3 := Sym(142)!(  3, 10)(  4, 11)(  5, 12)(  6, 13)(  7, 14)(  8, 15)(  9, 16)
( 17, 31)( 18, 32)( 19, 33)( 20, 34)( 21, 35)( 22, 36)( 23, 37)( 38, 45)
( 39, 46)( 40, 47)( 41, 48)( 42, 49)( 43, 50)( 44, 51)( 52, 66)( 53, 67)
( 54, 68)( 55, 69)( 56, 70)( 57, 71)( 58, 72)( 73, 80)( 74, 81)( 75, 82)
( 76, 83)( 77, 84)( 78, 85)( 79, 86)( 87,101)( 88,102)( 89,103)( 90,104)
( 91,105)( 92,106)( 93,107)(108,115)(109,116)(110,117)(111,118)(112,119)
(113,120)(114,121)(122,136)(123,137)(124,138)(125,139)(126,140)(127,141)
(128,142);
poly := sub<Sym(142)|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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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*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