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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}*784b
if this polytope has a 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 : 14
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}*392b
   4-fold quotients : {14,7}*196
   7-fold quotients : {2,28}*112
   14-fold quotients : {2,14}*56
   28-fold quotients : {2,7}*28
   49-fold quotients : {2,4}*16
   98-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {14,56}*1568b, {28,28}*1568b
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)(  2,112)(  3,111)(  4,110)(  5,109)(  6,108)(  7,107)(  8, 99)
(  9,105)( 10,104)( 11,103)( 12,102)( 13,101)( 14,100)( 15,141)( 16,147)
( 17,146)( 18,145)( 19,144)( 20,143)( 21,142)( 22,134)( 23,140)( 24,139)
( 25,138)( 26,137)( 27,136)( 28,135)( 29,127)( 30,133)( 31,132)( 32,131)
( 33,130)( 34,129)( 35,128)( 36,120)( 37,126)( 38,125)( 39,124)( 40,123)
( 41,122)( 42,121)( 43,113)( 44,119)( 45,118)( 46,117)( 47,116)( 48,115)
( 49,114)( 50,155)( 51,161)( 52,160)( 53,159)( 54,158)( 55,157)( 56,156)
( 57,148)( 58,154)( 59,153)( 60,152)( 61,151)( 62,150)( 63,149)( 64,190)
( 65,196)( 66,195)( 67,194)( 68,193)( 69,192)( 70,191)( 71,183)( 72,189)
( 73,188)( 74,187)( 75,186)( 76,185)( 77,184)( 78,176)( 79,182)( 80,181)
( 81,180)( 82,179)( 83,178)( 84,177)( 85,169)( 86,175)( 87,174)( 88,173)
( 89,172)( 90,171)( 91,170)( 92,162)( 93,168)( 94,167)( 95,166)( 96,165)
( 97,164)( 98,163);;
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, s2*s0*s1*s0*s1*s2*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*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)(  2,112)(  3,111)(  4,110)(  5,109)(  6,108)(  7,107)
(  8, 99)(  9,105)( 10,104)( 11,103)( 12,102)( 13,101)( 14,100)( 15,141)
( 16,147)( 17,146)( 18,145)( 19,144)( 20,143)( 21,142)( 22,134)( 23,140)
( 24,139)( 25,138)( 26,137)( 27,136)( 28,135)( 29,127)( 30,133)( 31,132)
( 32,131)( 33,130)( 34,129)( 35,128)( 36,120)( 37,126)( 38,125)( 39,124)
( 40,123)( 41,122)( 42,121)( 43,113)( 44,119)( 45,118)( 46,117)( 47,116)
( 48,115)( 49,114)( 50,155)( 51,161)( 52,160)( 53,159)( 54,158)( 55,157)
( 56,156)( 57,148)( 58,154)( 59,153)( 60,152)( 61,151)( 62,150)( 63,149)
( 64,190)( 65,196)( 66,195)( 67,194)( 68,193)( 69,192)( 70,191)( 71,183)
( 72,189)( 73,188)( 74,187)( 75,186)( 76,185)( 77,184)( 78,176)( 79,182)
( 80,181)( 81,180)( 82,179)( 83,178)( 84,177)( 85,169)( 86,175)( 87,174)
( 88,173)( 89,172)( 90,171)( 91,170)( 92,162)( 93,168)( 94,167)( 95,166)
( 96,165)( 97,164)( 98,163);
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, s2*s0*s1*s0*s1*s2*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*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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