Polytope of Type {194,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {194,2}*776
if this polytope has a name.
Group : SmallGroup(776,14)
Rank : 3
Schlafli Type : {194,2}
Number of vertices, edges, etc : 194, 194, 2
Order of s0s1s2 : 194
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {194,2,2} of size 1552
Vertex Figure Of :
   {2,194,2} of size 1552
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {97,2}*388
   97-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {194,4}*1552, {388,2}*1552
Permutation Representation (GAP) : 
s0 := (  2, 97)(  3, 96)(  4, 95)(  5, 94)(  6, 93)(  7, 92)(  8, 91)(  9, 90)
( 10, 89)( 11, 88)( 12, 87)( 13, 86)( 14, 85)( 15, 84)( 16, 83)( 17, 82)
( 18, 81)( 19, 80)( 20, 79)( 21, 78)( 22, 77)( 23, 76)( 24, 75)( 25, 74)
( 26, 73)( 27, 72)( 28, 71)( 29, 70)( 30, 69)( 31, 68)( 32, 67)( 33, 66)
( 34, 65)( 35, 64)( 36, 63)( 37, 62)( 38, 61)( 39, 60)( 40, 59)( 41, 58)
( 42, 57)( 43, 56)( 44, 55)( 45, 54)( 46, 53)( 47, 52)( 48, 51)( 49, 50)
( 99,194)(100,193)(101,192)(102,191)(103,190)(104,189)(105,188)(106,187)
(107,186)(108,185)(109,184)(110,183)(111,182)(112,181)(113,180)(114,179)
(115,178)(116,177)(117,176)(118,175)(119,174)(120,173)(121,172)(122,171)
(123,170)(124,169)(125,168)(126,167)(127,166)(128,165)(129,164)(130,163)
(131,162)(132,161)(133,160)(134,159)(135,158)(136,157)(137,156)(138,155)
(139,154)(140,153)(141,152)(142,151)(143,150)(144,149)(145,148)(146,147);;
s1 := (  1, 99)(  2, 98)(  3,194)(  4,193)(  5,192)(  6,191)(  7,190)(  8,189)
(  9,188)( 10,187)( 11,186)( 12,185)( 13,184)( 14,183)( 15,182)( 16,181)
( 17,180)( 18,179)( 19,178)( 20,177)( 21,176)( 22,175)( 23,174)( 24,173)
( 25,172)( 26,171)( 27,170)( 28,169)( 29,168)( 30,167)( 31,166)( 32,165)
( 33,164)( 34,163)( 35,162)( 36,161)( 37,160)( 38,159)( 39,158)( 40,157)
( 41,156)( 42,155)( 43,154)( 44,153)( 45,152)( 46,151)( 47,150)( 48,149)
( 49,148)( 50,147)( 51,146)( 52,145)( 53,144)( 54,143)( 55,142)( 56,141)
( 57,140)( 58,139)( 59,138)( 60,137)( 61,136)( 62,135)( 63,134)( 64,133)
( 65,132)( 66,131)( 67,130)( 68,129)( 69,128)( 70,127)( 71,126)( 72,125)
( 73,124)( 74,123)( 75,122)( 76,121)( 77,120)( 78,119)( 79,118)( 80,117)
( 81,116)( 82,115)( 83,114)( 84,113)( 85,112)( 86,111)( 87,110)( 88,109)
( 89,108)( 90,107)( 91,106)( 92,105)( 93,104)( 94,103)( 95,102)( 96,101)
( 97,100);;
s2 := (195,196);;
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, 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*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, 97)(  3, 96)(  4, 95)(  5, 94)(  6, 93)(  7, 92)(  8, 91)
(  9, 90)( 10, 89)( 11, 88)( 12, 87)( 13, 86)( 14, 85)( 15, 84)( 16, 83)
( 17, 82)( 18, 81)( 19, 80)( 20, 79)( 21, 78)( 22, 77)( 23, 76)( 24, 75)
( 25, 74)( 26, 73)( 27, 72)( 28, 71)( 29, 70)( 30, 69)( 31, 68)( 32, 67)
( 33, 66)( 34, 65)( 35, 64)( 36, 63)( 37, 62)( 38, 61)( 39, 60)( 40, 59)
( 41, 58)( 42, 57)( 43, 56)( 44, 55)( 45, 54)( 46, 53)( 47, 52)( 48, 51)
( 49, 50)( 99,194)(100,193)(101,192)(102,191)(103,190)(104,189)(105,188)
(106,187)(107,186)(108,185)(109,184)(110,183)(111,182)(112,181)(113,180)
(114,179)(115,178)(116,177)(117,176)(118,175)(119,174)(120,173)(121,172)
(122,171)(123,170)(124,169)(125,168)(126,167)(127,166)(128,165)(129,164)
(130,163)(131,162)(132,161)(133,160)(134,159)(135,158)(136,157)(137,156)
(138,155)(139,154)(140,153)(141,152)(142,151)(143,150)(144,149)(145,148)
(146,147);
s1 := Sym(196)!(  1, 99)(  2, 98)(  3,194)(  4,193)(  5,192)(  6,191)(  7,190)
(  8,189)(  9,188)( 10,187)( 11,186)( 12,185)( 13,184)( 14,183)( 15,182)
( 16,181)( 17,180)( 18,179)( 19,178)( 20,177)( 21,176)( 22,175)( 23,174)
( 24,173)( 25,172)( 26,171)( 27,170)( 28,169)( 29,168)( 30,167)( 31,166)
( 32,165)( 33,164)( 34,163)( 35,162)( 36,161)( 37,160)( 38,159)( 39,158)
( 40,157)( 41,156)( 42,155)( 43,154)( 44,153)( 45,152)( 46,151)( 47,150)
( 48,149)( 49,148)( 50,147)( 51,146)( 52,145)( 53,144)( 54,143)( 55,142)
( 56,141)( 57,140)( 58,139)( 59,138)( 60,137)( 61,136)( 62,135)( 63,134)
( 64,133)( 65,132)( 66,131)( 67,130)( 68,129)( 69,128)( 70,127)( 71,126)
( 72,125)( 73,124)( 74,123)( 75,122)( 76,121)( 77,120)( 78,119)( 79,118)
( 80,117)( 81,116)( 82,115)( 83,114)( 84,113)( 85,112)( 86,111)( 87,110)
( 88,109)( 89,108)( 90,107)( 91,106)( 92,105)( 93,104)( 94,103)( 95,102)
( 96,101)( 97,100);
s2 := Sym(196)!(195,196);
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, 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*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 >;

to this polytope