Polytope of Type {28,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,14}*784a
Also Known As : {28,14|2}. if this polytope has another name.
Group : SmallGroup(784,125)
Rank : 3
Schlafli Type : {28,14}
Number of vertices, edges, etc : 28, 196, 14
Order of s₀s₁s₂ : 28
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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}*392a
   7-fold quotients : {28,2}*112, {4,14}*112
   14-fold quotients : {2,14}*56, {14,2}*56
   28-fold quotients : {2,7}*28, {7,2}*28
   49-fold quotients : {4,2}*16
   98-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {56,14}*1568a, {28,28}*1568a
Permutation Representation (GAP) :

s0 := (  8, 43)(  9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 36)
( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)( 23, 30)
( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 57, 92)( 58, 93)( 59, 94)
( 60, 95)( 61, 96)( 62, 97)( 63, 98)( 64, 85)( 65, 86)( 66, 87)( 67, 88)
( 68, 89)( 69, 90)( 70, 91)( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)
( 76, 83)( 77, 84)( 99,148)(100,149)(101,150)(102,151)(103,152)(104,153)
(105,154)(106,190)(107,191)(108,192)(109,193)(110,194)(111,195)(112,196)
(113,183)(114,184)(115,185)(116,186)(117,187)(118,188)(119,189)(120,176)
(121,177)(122,178)(123,179)(124,180)(125,181)(126,182)(127,169)(128,170)
(129,171)(130,172)(131,173)(132,174)(133,175)(134,162)(135,163)(136,164)
(137,165)(138,166)(139,167)(140,168)(141,155)(142,156)(143,157)(144,158)
(145,159)(146,160)(147,161);;
s1 := (  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);;
s2 := (  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)
( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)( 36, 37)
( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)( 53, 55)
( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)( 73, 77)
( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)( 92, 93)
( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)(109,111)
(113,114)(115,119)(116,118)(120,121)(122,126)(123,125)(127,128)(129,133)
(130,132)(134,135)(136,140)(137,139)(141,142)(143,147)(144,146)(148,149)
(150,154)(151,153)(155,156)(157,161)(158,160)(162,163)(164,168)(165,167)
(169,170)(171,175)(172,174)(176,177)(178,182)(179,181)(183,184)(185,189)
(186,188)(190,191)(192,196)(193,195);;
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, 
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, 
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*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)!(  8, 43)(  9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)
( 15, 36)( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)
( 23, 30)( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 57, 92)( 58, 93)
( 59, 94)( 60, 95)( 61, 96)( 62, 97)( 63, 98)( 64, 85)( 65, 86)( 66, 87)
( 67, 88)( 68, 89)( 69, 90)( 70, 91)( 71, 78)( 72, 79)( 73, 80)( 74, 81)
( 75, 82)( 76, 83)( 77, 84)( 99,148)(100,149)(101,150)(102,151)(103,152)
(104,153)(105,154)(106,190)(107,191)(108,192)(109,193)(110,194)(111,195)
(112,196)(113,183)(114,184)(115,185)(116,186)(117,187)(118,188)(119,189)
(120,176)(121,177)(122,178)(123,179)(124,180)(125,181)(126,182)(127,169)
(128,170)(129,171)(130,172)(131,173)(132,174)(133,175)(134,162)(135,163)
(136,164)(137,165)(138,166)(139,167)(140,168)(141,155)(142,156)(143,157)
(144,158)(145,159)(146,160)(147,161);
s1 := 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);
s2 := Sym(196)!(  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)
( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)
( 36, 37)( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)
( 53, 55)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)
( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)
( 92, 93)( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)
(109,111)(113,114)(115,119)(116,118)(120,121)(122,126)(123,125)(127,128)
(129,133)(130,132)(134,135)(136,140)(137,139)(141,142)(143,147)(144,146)
(148,149)(150,154)(151,153)(155,156)(157,161)(158,160)(162,163)(164,168)
(165,167)(169,170)(171,175)(172,174)(176,177)(178,182)(179,181)(183,184)
(185,189)(186,188)(190,191)(192,196)(193,195);
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, 
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, 
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*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