Polytope of Type {28,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,14}*784b
if this polytope has a 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 : 14
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}*392c
   4-fold quotients : {7,14}*196
   7-fold quotients : {28,2}*112
   14-fold quotients : {14,2}*56
   28-fold quotients : {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}*1568b, {28,28}*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)
( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)(106,190)
(107,196)(108,195)(109,194)(110,193)(111,192)(112,191)(113,183)(114,189)
(115,188)(116,187)(117,186)(118,185)(119,184)(120,176)(121,182)(122,181)
(123,180)(124,179)(125,178)(126,177)(127,169)(128,175)(129,174)(130,173)
(131,172)(132,171)(133,170)(134,162)(135,168)(136,167)(137,166)(138,165)
(139,164)(140,163)(141,155)(142,161)(143,160)(144,159)(145,158)(146,157)
(147,156);;
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)(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);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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)!(  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)( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)
(106,190)(107,196)(108,195)(109,194)(110,193)(111,192)(112,191)(113,183)
(114,189)(115,188)(116,187)(117,186)(118,185)(119,184)(120,176)(121,182)
(122,181)(123,180)(124,179)(125,178)(126,177)(127,169)(128,175)(129,174)
(130,173)(131,172)(132,171)(133,170)(134,162)(135,168)(136,167)(137,166)
(138,165)(139,164)(140,163)(141,155)(142,161)(143,160)(144,159)(145,158)
(146,157)(147,156);
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)(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);
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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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