Part of the Atlas of Small Regular Polytopes

Polytope of Type {196,2}

Atlas Canonical Name {196,2}*784

Overview

Group
SmallGroup(784,29)
Rank
3
Schläfli Type
{196,2}
Vertices, edges, …
196, 196, 2
Order of s0s1s2
196
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

4-fold

7-fold

14-fold

28-fold

49-fold

98-fold

Covers minimal covers in bold

2-fold

Representations

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