Polytope of Type {98,4}

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

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