Polytope of Type {28,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,14}*784c
if this polytope has a name.
Group : SmallGroup(784,135)
Rank : 3
Schlafli Type : {28,14}
Number of vertices, edges, etc : 28, 196, 14
Order of s₀s₁s₂ : 28
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {28,14,2} of size 1568
Vertex Figure Of :
   {2,28,14} of size 1568
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {14,14}*392b
   4-fold quotients : {14,7}*196
   7-fold quotients : {4,14}*112
   14-fold quotients : {2,14}*56
   28-fold quotients : {2,7}*28
   49-fold quotients : {4,2}*16
   98-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {28,28}*1568b, {56,14}*1568c
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)( 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);;
s1 := (  1,100)(  2, 99)(  3,105)(  4,104)(  5,103)(  6,102)(  7,101)(  8,142)
(  9,141)( 10,147)( 11,146)( 12,145)( 13,144)( 14,143)( 15,135)( 16,134)
( 17,140)( 18,139)( 19,138)( 20,137)( 21,136)( 22,128)( 23,127)( 24,133)
( 25,132)( 26,131)( 27,130)( 28,129)( 29,121)( 30,120)( 31,126)( 32,125)
( 33,124)( 34,123)( 35,122)( 36,114)( 37,113)( 38,119)( 39,118)( 40,117)
( 41,116)( 42,115)( 43,107)( 44,106)( 45,112)( 46,111)( 47,110)( 48,109)
( 49,108)( 50,149)( 51,148)( 52,154)( 53,153)( 54,152)( 55,151)( 56,150)
( 57,191)( 58,190)( 59,196)( 60,195)( 61,194)( 62,193)( 63,192)( 64,184)
( 65,183)( 66,189)( 67,188)( 68,187)( 69,186)( 70,185)( 71,177)( 72,176)
( 73,182)( 74,181)( 75,180)( 76,179)( 77,178)( 78,170)( 79,169)( 80,175)
( 81,174)( 82,173)( 83,172)( 84,171)( 85,163)( 86,162)( 87,168)( 88,167)
( 89,166)( 90,165)( 91,164)( 92,156)( 93,155)( 94,161)( 95,160)( 96,159)
( 97,158)( 98,157);;
s2 := (  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 15, 43)
( 16, 49)( 17, 48)( 18, 47)( 19, 46)( 20, 45)( 21, 44)( 22, 36)( 23, 42)
( 24, 41)( 25, 40)( 26, 39)( 27, 38)( 28, 37)( 30, 35)( 31, 34)( 32, 33)
( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)( 64, 92)
( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71, 85)( 72, 91)
( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 79, 84)( 80, 83)( 81, 82)
( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,141)
(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,134)(121,140)
(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)(130,131)
(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(162,190)
(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)(169,183)(170,189)
(171,188)(172,187)(173,186)(174,185)(175,184)(177,182)(178,181)(179,180);;
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, 
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)( 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);
s1 := Sym(196)!(  1,100)(  2, 99)(  3,105)(  4,104)(  5,103)(  6,102)(  7,101)
(  8,142)(  9,141)( 10,147)( 11,146)( 12,145)( 13,144)( 14,143)( 15,135)
( 16,134)( 17,140)( 18,139)( 19,138)( 20,137)( 21,136)( 22,128)( 23,127)
( 24,133)( 25,132)( 26,131)( 27,130)( 28,129)( 29,121)( 30,120)( 31,126)
( 32,125)( 33,124)( 34,123)( 35,122)( 36,114)( 37,113)( 38,119)( 39,118)
( 40,117)( 41,116)( 42,115)( 43,107)( 44,106)( 45,112)( 46,111)( 47,110)
( 48,109)( 49,108)( 50,149)( 51,148)( 52,154)( 53,153)( 54,152)( 55,151)
( 56,150)( 57,191)( 58,190)( 59,196)( 60,195)( 61,194)( 62,193)( 63,192)
( 64,184)( 65,183)( 66,189)( 67,188)( 68,187)( 69,186)( 70,185)( 71,177)
( 72,176)( 73,182)( 74,181)( 75,180)( 76,179)( 77,178)( 78,170)( 79,169)
( 80,175)( 81,174)( 82,173)( 83,172)( 84,171)( 85,163)( 86,162)( 87,168)
( 88,167)( 89,166)( 90,165)( 91,164)( 92,156)( 93,155)( 94,161)( 95,160)
( 96,159)( 97,158)( 98,157);
s2 := Sym(196)!(  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)
( 15, 43)( 16, 49)( 17, 48)( 18, 47)( 19, 46)( 20, 45)( 21, 44)( 22, 36)
( 23, 42)( 24, 41)( 25, 40)( 26, 39)( 27, 38)( 28, 37)( 30, 35)( 31, 34)
( 32, 33)( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)
( 64, 92)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71, 85)
( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 79, 84)( 80, 83)
( 81, 82)( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)
(113,141)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,134)
(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)
(130,131)(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)
(162,190)(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)(169,183)
(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)(177,182)(178,181)
(179,180);
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, 
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.
to this polytope