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Polytope of Type {14,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,28}*784a
Also Known As : {14,28|2}. if this polytope has another name.
Group : SmallGroup(784,125)
Rank : 3
Schlafli Type : {14,28}
Number of vertices, edges, etc : 14, 196, 28
Order of s0s1s2 : 28
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {14,28,2} of size 1568
Vertex Figure Of :
   {2,14,28} of size 1568
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {14,14}*392a
   7-fold quotients : {2,28}*112, {14,4}*112
   14-fold quotients : {2,14}*56, {14,2}*56
   28-fold quotients : {2,7}*28, {7,2}*28
   49-fold quotients : {2,4}*16
   98-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {14,56}*1568a, {28,28}*1568a
Permutation Representation (GAP) :
s0 := (  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)
( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)
( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)
( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)( 73, 76)
( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)( 93, 98)
( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)(109,110)
(114,119)(115,118)(116,117)(121,126)(122,125)(123,124)(128,133)(129,132)
(130,131)(135,140)(136,139)(137,138)(142,147)(143,146)(144,145)(149,154)
(150,153)(151,152)(156,161)(157,160)(158,159)(163,168)(164,167)(165,166)
(170,175)(171,174)(172,173)(177,182)(178,181)(179,180)(184,189)(185,188)
(186,187)(191,196)(192,195)(193,194);;
s1 := (  1,  2)(  3,  7)(  4,  6)(  8, 44)(  9, 43)( 10, 49)( 11, 48)( 12, 47)
( 13, 46)( 14, 45)( 15, 37)( 16, 36)( 17, 42)( 18, 41)( 19, 40)( 20, 39)
( 21, 38)( 22, 30)( 23, 29)( 24, 35)( 25, 34)( 26, 33)( 27, 32)( 28, 31)
( 50, 51)( 52, 56)( 53, 55)( 57, 93)( 58, 92)( 59, 98)( 60, 97)( 61, 96)
( 62, 95)( 63, 94)( 64, 86)( 65, 85)( 66, 91)( 67, 90)( 68, 89)( 69, 88)
( 70, 87)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)
( 99,149)(100,148)(101,154)(102,153)(103,152)(104,151)(105,150)(106,191)
(107,190)(108,196)(109,195)(110,194)(111,193)(112,192)(113,184)(114,183)
(115,189)(116,188)(117,187)(118,186)(119,185)(120,177)(121,176)(122,182)
(123,181)(124,180)(125,179)(126,178)(127,170)(128,169)(129,175)(130,174)
(131,173)(132,172)(133,171)(134,163)(135,162)(136,168)(137,167)(138,166)
(139,165)(140,164)(141,156)(142,155)(143,161)(144,160)(145,159)(146,158)
(147,157);;
s2 := (  1,106)(  2,107)(  3,108)(  4,109)(  5,110)(  6,111)(  7,112)(  8, 99)
(  9,100)( 10,101)( 11,102)( 12,103)( 13,104)( 14,105)( 15,141)( 16,142)
( 17,143)( 18,144)( 19,145)( 20,146)( 21,147)( 22,134)( 23,135)( 24,136)
( 25,137)( 26,138)( 27,139)( 28,140)( 29,127)( 30,128)( 31,129)( 32,130)
( 33,131)( 34,132)( 35,133)( 36,120)( 37,121)( 38,122)( 39,123)( 40,124)
( 41,125)( 42,126)( 43,113)( 44,114)( 45,115)( 46,116)( 47,117)( 48,118)
( 49,119)( 50,155)( 51,156)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)
( 57,148)( 58,149)( 59,150)( 60,151)( 61,152)( 62,153)( 63,154)( 64,190)
( 65,191)( 66,192)( 67,193)( 68,194)( 69,195)( 70,196)( 71,183)( 72,184)
( 73,185)( 74,186)( 75,187)( 76,188)( 77,189)( 78,176)( 79,177)( 80,178)
( 81,179)( 82,180)( 83,181)( 84,182)( 85,169)( 86,170)( 87,171)( 88,172)
( 89,173)( 90,174)( 91,175)( 92,162)( 93,163)( 94,164)( 95,165)( 96,166)
( 97,167)( 98,168);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(196)!(  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)
( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)
( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)
( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)
( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)
( 93, 98)( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)
(109,110)(114,119)(115,118)(116,117)(121,126)(122,125)(123,124)(128,133)
(129,132)(130,131)(135,140)(136,139)(137,138)(142,147)(143,146)(144,145)
(149,154)(150,153)(151,152)(156,161)(157,160)(158,159)(163,168)(164,167)
(165,166)(170,175)(171,174)(172,173)(177,182)(178,181)(179,180)(184,189)
(185,188)(186,187)(191,196)(192,195)(193,194);
s1 := Sym(196)!(  1,  2)(  3,  7)(  4,  6)(  8, 44)(  9, 43)( 10, 49)( 11, 48)
( 12, 47)( 13, 46)( 14, 45)( 15, 37)( 16, 36)( 17, 42)( 18, 41)( 19, 40)
( 20, 39)( 21, 38)( 22, 30)( 23, 29)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 50, 51)( 52, 56)( 53, 55)( 57, 93)( 58, 92)( 59, 98)( 60, 97)
( 61, 96)( 62, 95)( 63, 94)( 64, 86)( 65, 85)( 66, 91)( 67, 90)( 68, 89)
( 69, 88)( 70, 87)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)
( 77, 80)( 99,149)(100,148)(101,154)(102,153)(103,152)(104,151)(105,150)
(106,191)(107,190)(108,196)(109,195)(110,194)(111,193)(112,192)(113,184)
(114,183)(115,189)(116,188)(117,187)(118,186)(119,185)(120,177)(121,176)
(122,182)(123,181)(124,180)(125,179)(126,178)(127,170)(128,169)(129,175)
(130,174)(131,173)(132,172)(133,171)(134,163)(135,162)(136,168)(137,167)
(138,166)(139,165)(140,164)(141,156)(142,155)(143,161)(144,160)(145,159)
(146,158)(147,157);
s2 := Sym(196)!(  1,106)(  2,107)(  3,108)(  4,109)(  5,110)(  6,111)(  7,112)
(  8, 99)(  9,100)( 10,101)( 11,102)( 12,103)( 13,104)( 14,105)( 15,141)
( 16,142)( 17,143)( 18,144)( 19,145)( 20,146)( 21,147)( 22,134)( 23,135)
( 24,136)( 25,137)( 26,138)( 27,139)( 28,140)( 29,127)( 30,128)( 31,129)
( 32,130)( 33,131)( 34,132)( 35,133)( 36,120)( 37,121)( 38,122)( 39,123)
( 40,124)( 41,125)( 42,126)( 43,113)( 44,114)( 45,115)( 46,116)( 47,117)
( 48,118)( 49,119)( 50,155)( 51,156)( 52,157)( 53,158)( 54,159)( 55,160)
( 56,161)( 57,148)( 58,149)( 59,150)( 60,151)( 61,152)( 62,153)( 63,154)
( 64,190)( 65,191)( 66,192)( 67,193)( 68,194)( 69,195)( 70,196)( 71,183)
( 72,184)( 73,185)( 74,186)( 75,187)( 76,188)( 77,189)( 78,176)( 79,177)
( 80,178)( 81,179)( 82,180)( 83,181)( 84,182)( 85,169)( 86,170)( 87,171)
( 88,172)( 89,173)( 90,174)( 91,175)( 92,162)( 93,163)( 94,164)( 95,165)
( 96,166)( 97,167)( 98,168);
poly := sub<Sym(196)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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 >; 
 
References : None.
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