Polytope of Type {4,98}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,98}*784
Also Known As : {4,98|2}. if this polytope has another name.
Group : SmallGroup(784,31)
Rank : 3
Schlafli Type : {4,98}
Number of vertices, edges, etc : 4, 196, 98
Order of s₀s₁s₂ : 196
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,98,2} of size 1568
Vertex Figure Of :
   {2,4,98} of size 1568
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,98}*392
   4-fold quotients : {2,49}*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 : {4,196}*1568, {8,98}*1568
Permutation Representation (GAP) :

s0 := ( 99,148)(100,149)(101,150)(102,151)(103,152)(104,153)(105,154)(106,155)
(107,156)(108,157)(109,158)(110,159)(111,160)(112,161)(113,162)(114,163)
(115,164)(116,165)(117,166)(118,167)(119,168)(120,169)(121,170)(122,171)
(123,172)(124,173)(125,174)(126,175)(127,176)(128,177)(129,178)(130,179)
(131,180)(132,181)(133,182)(134,183)(135,184)(136,185)(137,186)(138,187)
(139,188)(140,189)(141,190)(142,191)(143,192)(144,193)(145,194)(146,195)
(147,196);;
s1 := (  1, 99)(  2,105)(  3,104)(  4,103)(  5,102)(  6,101)(  7,100)(  8,147)
(  9,146)( 10,145)( 11,144)( 12,143)( 13,142)( 14,141)( 15,140)( 16,139)
( 17,138)( 18,137)( 19,136)( 20,135)( 21,134)( 22,133)( 23,132)( 24,131)
( 25,130)( 26,129)( 27,128)( 28,127)( 29,126)( 30,125)( 31,124)( 32,123)
( 33,122)( 34,121)( 35,120)( 36,119)( 37,118)( 38,117)( 39,116)( 40,115)
( 41,114)( 42,113)( 43,112)( 44,111)( 45,110)( 46,109)( 47,108)( 48,107)
( 49,106)( 50,148)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)( 56,149)
( 57,196)( 58,195)( 59,194)( 60,193)( 61,192)( 62,191)( 63,190)( 64,189)
( 65,188)( 66,187)( 67,186)( 68,185)( 69,184)( 70,183)( 71,182)( 72,181)
( 73,180)( 74,179)( 75,178)( 76,177)( 77,176)( 78,175)( 79,174)( 80,173)
( 81,172)( 82,171)( 83,170)( 84,169)( 85,168)( 86,167)( 87,166)( 88,165)
( 89,164)( 90,163)( 91,162)( 92,161)( 93,160)( 94,159)( 95,158)( 96,157)
( 97,156)( 98,155);;
s2 := (  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 15, 49)
( 16, 48)( 17, 47)( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)
( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 31, 33)
( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)( 64, 98)
( 65, 97)( 66, 96)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 91)( 72, 90)
( 73, 89)( 74, 88)( 75, 87)( 76, 86)( 77, 85)( 78, 84)( 79, 83)( 80, 82)
( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,147)
(114,146)(115,145)(116,144)(117,143)(118,142)(119,141)(120,140)(121,139)
(122,138)(123,137)(124,136)(125,135)(126,134)(127,133)(128,132)(129,131)
(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(162,196)
(163,195)(164,194)(165,193)(166,192)(167,191)(168,190)(169,189)(170,188)
(171,187)(172,186)(173,185)(174,184)(175,183)(176,182)(177,181)(178,180);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
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*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*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*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)!( 99,148)(100,149)(101,150)(102,151)(103,152)(104,153)(105,154)
(106,155)(107,156)(108,157)(109,158)(110,159)(111,160)(112,161)(113,162)
(114,163)(115,164)(116,165)(117,166)(118,167)(119,168)(120,169)(121,170)
(122,171)(123,172)(124,173)(125,174)(126,175)(127,176)(128,177)(129,178)
(130,179)(131,180)(132,181)(133,182)(134,183)(135,184)(136,185)(137,186)
(138,187)(139,188)(140,189)(141,190)(142,191)(143,192)(144,193)(145,194)
(146,195)(147,196);
s1 := Sym(196)!(  1, 99)(  2,105)(  3,104)(  4,103)(  5,102)(  6,101)(  7,100)
(  8,147)(  9,146)( 10,145)( 11,144)( 12,143)( 13,142)( 14,141)( 15,140)
( 16,139)( 17,138)( 18,137)( 19,136)( 20,135)( 21,134)( 22,133)( 23,132)
( 24,131)( 25,130)( 26,129)( 27,128)( 28,127)( 29,126)( 30,125)( 31,124)
( 32,123)( 33,122)( 34,121)( 35,120)( 36,119)( 37,118)( 38,117)( 39,116)
( 40,115)( 41,114)( 42,113)( 43,112)( 44,111)( 45,110)( 46,109)( 47,108)
( 48,107)( 49,106)( 50,148)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)
( 56,149)( 57,196)( 58,195)( 59,194)( 60,193)( 61,192)( 62,191)( 63,190)
( 64,189)( 65,188)( 66,187)( 67,186)( 68,185)( 69,184)( 70,183)( 71,182)
( 72,181)( 73,180)( 74,179)( 75,178)( 76,177)( 77,176)( 78,175)( 79,174)
( 80,173)( 81,172)( 82,171)( 83,170)( 84,169)( 85,168)( 86,167)( 87,166)
( 88,165)( 89,164)( 90,163)( 91,162)( 92,161)( 93,160)( 94,159)( 95,158)
( 96,157)( 97,156)( 98,155);
s2 := Sym(196)!(  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)
( 15, 49)( 16, 48)( 17, 47)( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 42)
( 23, 41)( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)
( 31, 33)( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)
( 64, 98)( 65, 97)( 66, 96)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 91)
( 72, 90)( 73, 89)( 74, 88)( 75, 87)( 76, 86)( 77, 85)( 78, 84)( 79, 83)
( 80, 82)( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)
(113,147)(114,146)(115,145)(116,144)(117,143)(118,142)(119,141)(120,140)
(121,139)(122,138)(123,137)(124,136)(125,135)(126,134)(127,133)(128,132)
(129,131)(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)
(162,196)(163,195)(164,194)(165,193)(166,192)(167,191)(168,190)(169,189)
(170,188)(171,187)(172,186)(173,185)(174,184)(175,183)(176,182)(177,181)
(178,180);
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, s0*s1*s0*s1*s0*s1*s0*s1, 
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*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*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*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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