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