Part of the Atlas of Small Regular Polytopes

Polytope of Type {194,2}

Atlas Canonical Name {194,2}*776

Overview

Group
SmallGroup(776,14)
Rank
3
Schläfli Type
{194,2}
Vertices, edges, …
194, 194, 2
Order of s0s1s2
194
Order of s0s1s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat
  • Self-Petrie

Quotients maximal quotients in bold

2-fold

97-fold

Covers minimal covers in bold

2-fold

Representations

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 >;