Part of the Atlas of Small Regular Polytopes

Polytope of Type {188}

Atlas Canonical Name {188}*376

Overview

Group
SmallGroup(376,5)
Rank
2
Schläfli Type
{188}
Vertices, edges, …
188, 188
Order of s0s1
188
Also known as
188-gon, {188}. if this polytope has another name.

Special Properties

  • Universal
  • Spherical
  • Locally Spherical
  • Orientable
  • Self-Dual

Quotients maximal quotients in bold

2-fold

4-fold

47-fold

94-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.