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Polytope of Type {2,14,28}

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

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