Polytope of Type {2,98,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,98,4}*1568
if this polytope has a name.
Group : SmallGroup(1568,181)
Rank : 4
Schlafli Type : {2,98,4}
Number of vertices, edges, etc : 2, 98, 196, 4
Order of s₀s₁s₂s₃ : 196
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,98,2}*784
   4-fold quotients : {2,49,2}*392
   7-fold quotients : {2,14,4}*224
   14-fold quotients : {2,14,2}*112
   28-fold quotients : {2,7,2}*56
   49-fold quotients : {2,2,4}*32
   98-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  9)(  5,  8)(  6,  7)( 10, 51)( 11, 50)( 12, 49)( 13, 48)( 14, 47)
( 15, 46)( 16, 45)( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 40)( 22, 39)
( 23, 38)( 24, 37)( 25, 36)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)
( 53, 58)( 54, 57)( 55, 56)( 59,100)( 60, 99)( 61, 98)( 62, 97)( 63, 96)
( 64, 95)( 65, 94)( 66, 93)( 67, 92)( 68, 91)( 69, 90)( 70, 89)( 71, 88)
( 72, 87)( 73, 86)( 74, 85)( 75, 84)( 76, 83)( 77, 82)( 78, 81)( 79, 80)
(102,107)(103,106)(104,105)(108,149)(109,148)(110,147)(111,146)(112,145)
(113,144)(114,143)(115,142)(116,141)(117,140)(118,139)(119,138)(120,137)
(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)
(151,156)(152,155)(153,154)(157,198)(158,197)(159,196)(160,195)(161,194)
(162,193)(163,192)(164,191)(165,190)(166,189)(167,188)(168,187)(169,186)
(170,185)(171,184)(172,183)(173,182)(174,181)(175,180)(176,179)(177,178);;
s2 := (  3, 10)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 17, 51)
( 18, 50)( 19, 49)( 20, 48)( 21, 47)( 22, 46)( 23, 45)( 24, 44)( 25, 43)
( 26, 42)( 27, 41)( 28, 40)( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)
( 52, 59)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)( 58, 60)( 66,100)
( 67, 99)( 68, 98)( 69, 97)( 70, 96)( 71, 95)( 72, 94)( 73, 93)( 74, 92)
( 75, 91)( 76, 90)( 77, 89)( 78, 88)( 79, 87)( 80, 86)( 81, 85)( 82, 84)
(101,157)(102,163)(103,162)(104,161)(105,160)(106,159)(107,158)(108,150)
(109,156)(110,155)(111,154)(112,153)(113,152)(114,151)(115,198)(116,197)
(117,196)(118,195)(119,194)(120,193)(121,192)(122,191)(123,190)(124,189)
(125,188)(126,187)(127,186)(128,185)(129,184)(130,183)(131,182)(132,181)
(133,180)(134,179)(135,178)(136,177)(137,176)(138,175)(139,174)(140,173)
(141,172)(142,171)(143,170)(144,169)(145,168)(146,167)(147,166)(148,165)
(149,164);;
s3 := (  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)
( 99,197)(100,198);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
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(198)!(1,2);
s1 := Sym(198)!(  4,  9)(  5,  8)(  6,  7)( 10, 51)( 11, 50)( 12, 49)( 13, 48)
( 14, 47)( 15, 46)( 16, 45)( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 40)
( 22, 39)( 23, 38)( 24, 37)( 25, 36)( 26, 35)( 27, 34)( 28, 33)( 29, 32)
( 30, 31)( 53, 58)( 54, 57)( 55, 56)( 59,100)( 60, 99)( 61, 98)( 62, 97)
( 63, 96)( 64, 95)( 65, 94)( 66, 93)( 67, 92)( 68, 91)( 69, 90)( 70, 89)
( 71, 88)( 72, 87)( 73, 86)( 74, 85)( 75, 84)( 76, 83)( 77, 82)( 78, 81)
( 79, 80)(102,107)(103,106)(104,105)(108,149)(109,148)(110,147)(111,146)
(112,145)(113,144)(114,143)(115,142)(116,141)(117,140)(118,139)(119,138)
(120,137)(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)
(128,129)(151,156)(152,155)(153,154)(157,198)(158,197)(159,196)(160,195)
(161,194)(162,193)(163,192)(164,191)(165,190)(166,189)(167,188)(168,187)
(169,186)(170,185)(171,184)(172,183)(173,182)(174,181)(175,180)(176,179)
(177,178);
s2 := Sym(198)!(  3, 10)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)
( 17, 51)( 18, 50)( 19, 49)( 20, 48)( 21, 47)( 22, 46)( 23, 45)( 24, 44)
( 25, 43)( 26, 42)( 27, 41)( 28, 40)( 29, 39)( 30, 38)( 31, 37)( 32, 36)
( 33, 35)( 52, 59)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)( 58, 60)
( 66,100)( 67, 99)( 68, 98)( 69, 97)( 70, 96)( 71, 95)( 72, 94)( 73, 93)
( 74, 92)( 75, 91)( 76, 90)( 77, 89)( 78, 88)( 79, 87)( 80, 86)( 81, 85)
( 82, 84)(101,157)(102,163)(103,162)(104,161)(105,160)(106,159)(107,158)
(108,150)(109,156)(110,155)(111,154)(112,153)(113,152)(114,151)(115,198)
(116,197)(117,196)(118,195)(119,194)(120,193)(121,192)(122,191)(123,190)
(124,189)(125,188)(126,187)(127,186)(128,185)(129,184)(130,183)(131,182)
(132,181)(133,180)(134,179)(135,178)(136,177)(137,176)(138,175)(139,174)
(140,173)(141,172)(142,171)(143,170)(144,169)(145,168)(146,167)(147,166)
(148,165)(149,164);
s3 := Sym(198)!(  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)( 99,197)(100,198);
poly := sub<Sym(198)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, 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 >;

to this polytope