Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,94}

Atlas Canonical Name {4,94}*752

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(752,31)
Rank
3
Schläfli Type
{4,94}
Vertices, edges, …
4, 188, 94
Order of s0s1s2
188
Order of s0s1s2s1
2
Also known as
{4,94|2}. if this polytope has another name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

47-fold

94-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle