Polytope of Type {94,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {94,4}*752
Also Known As : {94,4|2}. if this polytope has another name.
Group : SmallGroup(752,31)
Rank : 3
Schlafli Type : {94,4}
Number of vertices, edges, etc : 94, 188, 4
Order of s₀s₁s₂ : 188
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {94,4,2} of size 1504
Vertex Figure Of :
   {2,94,4} of size 1504
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {94,2}*376
   4-fold quotients : {47,2}*188
   47-fold quotients : {2,4}*16
   94-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {188,4}*1504, {94,8}*1504
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)( 96,141)( 97,140)
( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)(104,133)(105,132)
(106,131)(107,130)(108,129)(109,128)(110,127)(111,126)(112,125)(113,124)
(114,123)(115,122)(116,121)(117,120)(118,119)(143,188)(144,187)(145,186)
(146,185)(147,184)(148,183)(149,182)(150,181)(151,180)(152,179)(153,178)
(154,177)(155,176)(156,175)(157,174)(158,173)(159,172)(160,171)(161,170)
(162,169)(163,168)(164,167)(165,166);;
s1 := (  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)( 95,143)( 96,142)
( 97,188)( 98,187)( 99,186)(100,185)(101,184)(102,183)(103,182)(104,181)
(105,180)(106,179)(107,178)(108,177)(109,176)(110,175)(111,174)(112,173)
(113,172)(114,171)(115,170)(116,169)(117,168)(118,167)(119,166)(120,165)
(121,164)(122,163)(123,162)(124,161)(125,160)(126,159)(127,158)(128,157)
(129,156)(130,155)(131,154)(132,153)(133,152)(134,151)(135,150)(136,149)
(137,148)(138,147)(139,146)(140,145)(141,144);;
s2 := (  1, 95)(  2, 96)(  3, 97)(  4, 98)(  5, 99)(  6,100)(  7,101)(  8,102)
(  9,103)( 10,104)( 11,105)( 12,106)( 13,107)( 14,108)( 15,109)( 16,110)
( 17,111)( 18,112)( 19,113)( 20,114)( 21,115)( 22,116)( 23,117)( 24,118)
( 25,119)( 26,120)( 27,121)( 28,122)( 29,123)( 30,124)( 31,125)( 32,126)
( 33,127)( 34,128)( 35,129)( 36,130)( 37,131)( 38,132)( 39,133)( 40,134)
( 41,135)( 42,136)( 43,137)( 44,138)( 45,139)( 46,140)( 47,141)( 48,142)
( 49,143)( 50,144)( 51,145)( 52,146)( 53,147)( 54,148)( 55,149)( 56,150)
( 57,151)( 58,152)( 59,153)( 60,154)( 61,155)( 62,156)( 63,157)( 64,158)
( 65,159)( 66,160)( 67,161)( 68,162)( 69,163)( 70,164)( 71,165)( 72,166)
( 73,167)( 74,168)( 75,169)( 76,170)( 77,171)( 78,172)( 79,173)( 80,174)
( 81,175)( 82,176)( 83,177)( 84,178)( 85,179)( 86,180)( 87,181)( 88,182)
( 89,183)( 90,184)( 91,185)( 92,186)( 93,187)( 94,188);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*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 ];;
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)( 96,141)
( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)(104,133)
(105,132)(106,131)(107,130)(108,129)(109,128)(110,127)(111,126)(112,125)
(113,124)(114,123)(115,122)(116,121)(117,120)(118,119)(143,188)(144,187)
(145,186)(146,185)(147,184)(148,183)(149,182)(150,181)(151,180)(152,179)
(153,178)(154,177)(155,176)(156,175)(157,174)(158,173)(159,172)(160,171)
(161,170)(162,169)(163,168)(164,167)(165,166);
s1 := 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)( 95,143)
( 96,142)( 97,188)( 98,187)( 99,186)(100,185)(101,184)(102,183)(103,182)
(104,181)(105,180)(106,179)(107,178)(108,177)(109,176)(110,175)(111,174)
(112,173)(113,172)(114,171)(115,170)(116,169)(117,168)(118,167)(119,166)
(120,165)(121,164)(122,163)(123,162)(124,161)(125,160)(126,159)(127,158)
(128,157)(129,156)(130,155)(131,154)(132,153)(133,152)(134,151)(135,150)
(136,149)(137,148)(138,147)(139,146)(140,145)(141,144);
s2 := Sym(188)!(  1, 95)(  2, 96)(  3, 97)(  4, 98)(  5, 99)(  6,100)(  7,101)
(  8,102)(  9,103)( 10,104)( 11,105)( 12,106)( 13,107)( 14,108)( 15,109)
( 16,110)( 17,111)( 18,112)( 19,113)( 20,114)( 21,115)( 22,116)( 23,117)
( 24,118)( 25,119)( 26,120)( 27,121)( 28,122)( 29,123)( 30,124)( 31,125)
( 32,126)( 33,127)( 34,128)( 35,129)( 36,130)( 37,131)( 38,132)( 39,133)
( 40,134)( 41,135)( 42,136)( 43,137)( 44,138)( 45,139)( 46,140)( 47,141)
( 48,142)( 49,143)( 50,144)( 51,145)( 52,146)( 53,147)( 54,148)( 55,149)
( 56,150)( 57,151)( 58,152)( 59,153)( 60,154)( 61,155)( 62,156)( 63,157)
( 64,158)( 65,159)( 66,160)( 67,161)( 68,162)( 69,163)( 70,164)( 71,165)
( 72,166)( 73,167)( 74,168)( 75,169)( 76,170)( 77,171)( 78,172)( 79,173)
( 80,174)( 81,175)( 82,176)( 83,177)( 84,178)( 85,179)( 86,180)( 87,181)
( 88,182)( 89,183)( 90,184)( 91,185)( 92,186)( 93,187)( 94,188);
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*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 >;

References : None.
to this polytope