Polytope of Type {2,14,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,28}*1568b
if this polytope has a name.
Group : SmallGroup(1568,851)
Rank : 4
Schlafli Type : {2,14,28}
Number of vertices, edges, etc : 2, 14, 196, 28
Order of s₀s₁s₂s₃ : 28
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 : {2,14,14}*784b
   4-fold quotients : {2,14,7}*392
   7-fold quotients : {2,2,28}*224
   14-fold quotients : {2,2,14}*112
   28-fold quotients : {2,2,7}*56
   49-fold quotients : {2,2,4}*32
   98-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)( 74, 79)( 75, 78)
( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)( 95,100)
( 96, 99)( 97, 98)(102,107)(103,106)(104,105)(109,114)(110,113)(111,112)
(116,121)(117,120)(118,119)(123,128)(124,127)(125,126)(130,135)(131,134)
(132,133)(137,142)(138,141)(139,140)(144,149)(145,148)(146,147)(151,156)
(152,155)(153,154)(158,163)(159,162)(160,161)(165,170)(166,169)(167,168)
(172,177)(173,176)(174,175)(179,184)(180,183)(181,182)(186,191)(187,190)
(188,189)(193,198)(194,197)(195,196);;
s2 := (  3,  4)(  5,  9)(  6,  8)( 10, 46)( 11, 45)( 12, 51)( 13, 50)( 14, 49)
( 15, 48)( 16, 47)( 17, 39)( 18, 38)( 19, 44)( 20, 43)( 21, 42)( 22, 41)
( 23, 40)( 24, 32)( 25, 31)( 26, 37)( 27, 36)( 28, 35)( 29, 34)( 30, 33)
( 52, 53)( 54, 58)( 55, 57)( 59, 95)( 60, 94)( 61,100)( 62, 99)( 63, 98)
( 64, 97)( 65, 96)( 66, 88)( 67, 87)( 68, 93)( 69, 92)( 70, 91)( 71, 90)
( 72, 89)( 73, 81)( 74, 80)( 75, 86)( 76, 85)( 77, 84)( 78, 83)( 79, 82)
(101,151)(102,150)(103,156)(104,155)(105,154)(106,153)(107,152)(108,193)
(109,192)(110,198)(111,197)(112,196)(113,195)(114,194)(115,186)(116,185)
(117,191)(118,190)(119,189)(120,188)(121,187)(122,179)(123,178)(124,184)
(125,183)(126,182)(127,181)(128,180)(129,172)(130,171)(131,177)(132,176)
(133,175)(134,174)(135,173)(136,165)(137,164)(138,170)(139,169)(140,168)
(141,167)(142,166)(143,158)(144,157)(145,163)(146,162)(147,161)(148,160)
(149,159);;
s3 := (  3,108)(  4,114)(  5,113)(  6,112)(  7,111)(  8,110)(  9,109)( 10,101)
( 11,107)( 12,106)( 13,105)( 14,104)( 15,103)( 16,102)( 17,143)( 18,149)
( 19,148)( 20,147)( 21,146)( 22,145)( 23,144)( 24,136)( 25,142)( 26,141)
( 27,140)( 28,139)( 29,138)( 30,137)( 31,129)( 32,135)( 33,134)( 34,133)
( 35,132)( 36,131)( 37,130)( 38,122)( 39,128)( 40,127)( 41,126)( 42,125)
( 43,124)( 44,123)( 45,115)( 46,121)( 47,120)( 48,119)( 49,118)( 50,117)
( 51,116)( 52,157)( 53,163)( 54,162)( 55,161)( 56,160)( 57,159)( 58,158)
( 59,150)( 60,156)( 61,155)( 62,154)( 63,153)( 64,152)( 65,151)( 66,192)
( 67,198)( 68,197)( 69,196)( 70,195)( 71,194)( 72,193)( 73,185)( 74,191)
( 75,190)( 76,189)( 77,188)( 78,187)( 79,186)( 80,178)( 81,184)( 82,183)
( 83,182)( 84,181)( 85,180)( 86,179)( 87,171)( 88,177)( 89,176)( 90,175)
( 91,174)( 92,173)( 93,172)( 94,164)( 95,170)( 96,169)( 97,168)( 98,167)
( 99,166)(100,165);;
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, 
s3*s1*s2*s1*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, 
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(198)!(1,2);
s1 := Sym(198)!(  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)( 74, 79)
( 75, 78)( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)
( 95,100)( 96, 99)( 97, 98)(102,107)(103,106)(104,105)(109,114)(110,113)
(111,112)(116,121)(117,120)(118,119)(123,128)(124,127)(125,126)(130,135)
(131,134)(132,133)(137,142)(138,141)(139,140)(144,149)(145,148)(146,147)
(151,156)(152,155)(153,154)(158,163)(159,162)(160,161)(165,170)(166,169)
(167,168)(172,177)(173,176)(174,175)(179,184)(180,183)(181,182)(186,191)
(187,190)(188,189)(193,198)(194,197)(195,196);
s2 := Sym(198)!(  3,  4)(  5,  9)(  6,  8)( 10, 46)( 11, 45)( 12, 51)( 13, 50)
( 14, 49)( 15, 48)( 16, 47)( 17, 39)( 18, 38)( 19, 44)( 20, 43)( 21, 42)
( 22, 41)( 23, 40)( 24, 32)( 25, 31)( 26, 37)( 27, 36)( 28, 35)( 29, 34)
( 30, 33)( 52, 53)( 54, 58)( 55, 57)( 59, 95)( 60, 94)( 61,100)( 62, 99)
( 63, 98)( 64, 97)( 65, 96)( 66, 88)( 67, 87)( 68, 93)( 69, 92)( 70, 91)
( 71, 90)( 72, 89)( 73, 81)( 74, 80)( 75, 86)( 76, 85)( 77, 84)( 78, 83)
( 79, 82)(101,151)(102,150)(103,156)(104,155)(105,154)(106,153)(107,152)
(108,193)(109,192)(110,198)(111,197)(112,196)(113,195)(114,194)(115,186)
(116,185)(117,191)(118,190)(119,189)(120,188)(121,187)(122,179)(123,178)
(124,184)(125,183)(126,182)(127,181)(128,180)(129,172)(130,171)(131,177)
(132,176)(133,175)(134,174)(135,173)(136,165)(137,164)(138,170)(139,169)
(140,168)(141,167)(142,166)(143,158)(144,157)(145,163)(146,162)(147,161)
(148,160)(149,159);
s3 := Sym(198)!(  3,108)(  4,114)(  5,113)(  6,112)(  7,111)(  8,110)(  9,109)
( 10,101)( 11,107)( 12,106)( 13,105)( 14,104)( 15,103)( 16,102)( 17,143)
( 18,149)( 19,148)( 20,147)( 21,146)( 22,145)( 23,144)( 24,136)( 25,142)
( 26,141)( 27,140)( 28,139)( 29,138)( 30,137)( 31,129)( 32,135)( 33,134)
( 34,133)( 35,132)( 36,131)( 37,130)( 38,122)( 39,128)( 40,127)( 41,126)
( 42,125)( 43,124)( 44,123)( 45,115)( 46,121)( 47,120)( 48,119)( 49,118)
( 50,117)( 51,116)( 52,157)( 53,163)( 54,162)( 55,161)( 56,160)( 57,159)
( 58,158)( 59,150)( 60,156)( 61,155)( 62,154)( 63,153)( 64,152)( 65,151)
( 66,192)( 67,198)( 68,197)( 69,196)( 70,195)( 71,194)( 72,193)( 73,185)
( 74,191)( 75,190)( 76,189)( 77,188)( 78,187)( 79,186)( 80,178)( 81,184)
( 82,183)( 83,182)( 84,181)( 85,180)( 86,179)( 87,171)( 88,177)( 89,176)
( 90,175)( 91,174)( 92,173)( 93,172)( 94,164)( 95,170)( 96,169)( 97,168)
( 98,167)( 99,166)(100,165);
poly := sub<Sym(198)|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, s3*s1*s2*s1*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, 
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