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Polytope of Type {2,28,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,28,14}*1568c
if this polytope has a name.
Group : SmallGroup(1568,877)
Rank : 4
Schlafli Type : {2,28,14}
Number of vertices, edges, etc : 2, 28, 196, 14
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 : {2,4,14}*224
   14-fold quotients : {2,2,14}*112
   28-fold quotients : {2,2,7}*56
   49-fold quotients : {2,4,2}*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)(101,150)(102,156)(103,155)(104,154)(105,153)(106,152)
(107,151)(108,157)(109,163)(110,162)(111,161)(112,160)(113,159)(114,158)
(115,164)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)(122,171)
(123,177)(124,176)(125,175)(126,174)(127,173)(128,172)(129,178)(130,184)
(131,183)(132,182)(133,181)(134,180)(135,179)(136,185)(137,191)(138,190)
(139,189)(140,188)(141,187)(142,186)(143,192)(144,198)(145,197)(146,196)
(147,195)(148,194)(149,193);;
s2 := (  3,102)(  4,101)(  5,107)(  6,106)(  7,105)(  8,104)(  9,103)( 10,144)
( 11,143)( 12,149)( 13,148)( 14,147)( 15,146)( 16,145)( 17,137)( 18,136)
( 19,142)( 20,141)( 21,140)( 22,139)( 23,138)( 24,130)( 25,129)( 26,135)
( 27,134)( 28,133)( 29,132)( 30,131)( 31,123)( 32,122)( 33,128)( 34,127)
( 35,126)( 36,125)( 37,124)( 38,116)( 39,115)( 40,121)( 41,120)( 42,119)
( 43,118)( 44,117)( 45,109)( 46,108)( 47,114)( 48,113)( 49,112)( 50,111)
( 51,110)( 52,151)( 53,150)( 54,156)( 55,155)( 56,154)( 57,153)( 58,152)
( 59,193)( 60,192)( 61,198)( 62,197)( 63,196)( 64,195)( 65,194)( 66,186)
( 67,185)( 68,191)( 69,190)( 70,189)( 71,188)( 72,187)( 73,179)( 74,178)
( 75,184)( 76,183)( 77,182)( 78,181)( 79,180)( 80,172)( 81,171)( 82,177)
( 83,176)( 84,175)( 85,174)( 86,173)( 87,165)( 88,164)( 89,170)( 90,169)
( 91,168)( 92,167)( 93,166)( 94,158)( 95,157)( 96,163)( 97,162)( 98,161)
( 99,160)(100,159);;
s3 := (  3, 10)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 17, 45)
( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)( 23, 46)( 24, 38)( 25, 44)
( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 32, 37)( 33, 36)( 34, 35)
( 52, 59)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)( 58, 60)( 66, 94)
( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)( 72, 95)( 73, 87)( 74, 93)
( 75, 92)( 76, 91)( 77, 90)( 78, 89)( 79, 88)( 81, 86)( 82, 85)( 83, 84)
(101,108)(102,114)(103,113)(104,112)(105,111)(106,110)(107,109)(115,143)
(116,149)(117,148)(118,147)(119,146)(120,145)(121,144)(122,136)(123,142)
(124,141)(125,140)(126,139)(127,138)(128,137)(130,135)(131,134)(132,133)
(150,157)(151,163)(152,162)(153,161)(154,160)(155,159)(156,158)(164,192)
(165,198)(166,197)(167,196)(168,195)(169,194)(170,193)(171,185)(172,191)
(173,190)(174,189)(175,188)(176,187)(177,186)(179,184)(180,183)(181,182);;
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, 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)(101,150)(102,156)(103,155)(104,154)(105,153)
(106,152)(107,151)(108,157)(109,163)(110,162)(111,161)(112,160)(113,159)
(114,158)(115,164)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)
(122,171)(123,177)(124,176)(125,175)(126,174)(127,173)(128,172)(129,178)
(130,184)(131,183)(132,182)(133,181)(134,180)(135,179)(136,185)(137,191)
(138,190)(139,189)(140,188)(141,187)(142,186)(143,192)(144,198)(145,197)
(146,196)(147,195)(148,194)(149,193);
s2 := Sym(198)!(  3,102)(  4,101)(  5,107)(  6,106)(  7,105)(  8,104)(  9,103)
( 10,144)( 11,143)( 12,149)( 13,148)( 14,147)( 15,146)( 16,145)( 17,137)
( 18,136)( 19,142)( 20,141)( 21,140)( 22,139)( 23,138)( 24,130)( 25,129)
( 26,135)( 27,134)( 28,133)( 29,132)( 30,131)( 31,123)( 32,122)( 33,128)
( 34,127)( 35,126)( 36,125)( 37,124)( 38,116)( 39,115)( 40,121)( 41,120)
( 42,119)( 43,118)( 44,117)( 45,109)( 46,108)( 47,114)( 48,113)( 49,112)
( 50,111)( 51,110)( 52,151)( 53,150)( 54,156)( 55,155)( 56,154)( 57,153)
( 58,152)( 59,193)( 60,192)( 61,198)( 62,197)( 63,196)( 64,195)( 65,194)
( 66,186)( 67,185)( 68,191)( 69,190)( 70,189)( 71,188)( 72,187)( 73,179)
( 74,178)( 75,184)( 76,183)( 77,182)( 78,181)( 79,180)( 80,172)( 81,171)
( 82,177)( 83,176)( 84,175)( 85,174)( 86,173)( 87,165)( 88,164)( 89,170)
( 90,169)( 91,168)( 92,167)( 93,166)( 94,158)( 95,157)( 96,163)( 97,162)
( 98,161)( 99,160)(100,159);
s3 := Sym(198)!(  3, 10)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)
( 17, 45)( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)( 23, 46)( 24, 38)
( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 32, 37)( 33, 36)
( 34, 35)( 52, 59)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)( 58, 60)
( 66, 94)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)( 72, 95)( 73, 87)
( 74, 93)( 75, 92)( 76, 91)( 77, 90)( 78, 89)( 79, 88)( 81, 86)( 82, 85)
( 83, 84)(101,108)(102,114)(103,113)(104,112)(105,111)(106,110)(107,109)
(115,143)(116,149)(117,148)(118,147)(119,146)(120,145)(121,144)(122,136)
(123,142)(124,141)(125,140)(126,139)(127,138)(128,137)(130,135)(131,134)
(132,133)(150,157)(151,163)(152,162)(153,161)(154,160)(155,159)(156,158)
(164,192)(165,198)(166,197)(167,196)(168,195)(169,194)(170,193)(171,185)
(172,191)(173,190)(174,189)(175,188)(176,187)(177,186)(179,184)(180,183)
(181,182);
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, 
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 >; 
 

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