Part of the Atlas of Small Regular Polytopes

Polytope of Type {190,2}

Atlas Canonical Name {190,2}*760

Overview

Group
SmallGroup(760,38)
Rank
3
Schläfli Type
{190,2}
Vertices, edges, …
190, 190, 2
Order of s0s1s2
190
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

5-fold

10-fold

19-fold

38-fold

95-fold

Covers minimal covers in bold

2-fold

Representations

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