Polytope of Type {2,94,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,94,4}*1504
if this polytope has a name.
Group : SmallGroup(1504,182)
Rank : 4
Schlafli Type : {2,94,4}
Number of vertices, edges, etc : 2, 94, 188, 4
Order of s₀s₁s₂s₃ : 188
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,94,2}*752
   4-fold quotients : {2,47,2}*376
   47-fold quotients : {2,2,4}*32
   94-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 49)(  5, 48)(  6, 47)(  7, 46)(  8, 45)(  9, 44)( 10, 43)( 11, 42)
( 12, 41)( 13, 40)( 14, 39)( 15, 38)( 16, 37)( 17, 36)( 18, 35)( 19, 34)
( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)( 26, 27)( 51, 96)
( 52, 95)( 53, 94)( 54, 93)( 55, 92)( 56, 91)( 57, 90)( 58, 89)( 59, 88)
( 60, 87)( 61, 86)( 62, 85)( 63, 84)( 64, 83)( 65, 82)( 66, 81)( 67, 80)
( 68, 79)( 69, 78)( 70, 77)( 71, 76)( 72, 75)( 73, 74)( 98,143)( 99,142)
(100,141)(101,140)(102,139)(103,138)(104,137)(105,136)(106,135)(107,134)
(108,133)(109,132)(110,131)(111,130)(112,129)(113,128)(114,127)(115,126)
(116,125)(117,124)(118,123)(119,122)(120,121)(145,190)(146,189)(147,188)
(148,187)(149,186)(150,185)(151,184)(152,183)(153,182)(154,181)(155,180)
(156,179)(157,178)(158,177)(159,176)(160,175)(161,174)(162,173)(163,172)
(164,171)(165,170)(166,169)(167,168);;
s2 := (  3,  4)(  5, 49)(  6, 48)(  7, 47)(  8, 46)(  9, 45)( 10, 44)( 11, 43)
( 12, 42)( 13, 41)( 14, 40)( 15, 39)( 16, 38)( 17, 37)( 18, 36)( 19, 35)
( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)( 26, 28)( 50, 51)
( 52, 96)( 53, 95)( 54, 94)( 55, 93)( 56, 92)( 57, 91)( 58, 90)( 59, 89)
( 60, 88)( 61, 87)( 62, 86)( 63, 85)( 64, 84)( 65, 83)( 66, 82)( 67, 81)
( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)( 73, 75)( 97,145)( 98,144)
( 99,190)(100,189)(101,188)(102,187)(103,186)(104,185)(105,184)(106,183)
(107,182)(108,181)(109,180)(110,179)(111,178)(112,177)(113,176)(114,175)
(115,174)(116,173)(117,172)(118,171)(119,170)(120,169)(121,168)(122,167)
(123,166)(124,165)(125,164)(126,163)(127,162)(128,161)(129,160)(130,159)
(131,158)(132,157)(133,156)(134,155)(135,154)(136,153)(137,152)(138,151)
(139,150)(140,149)(141,148)(142,147)(143,146);;
s3 := (  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)( 95,189)( 96,190);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
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(190)!(1,2);
s1 := Sym(190)!(  4, 49)(  5, 48)(  6, 47)(  7, 46)(  8, 45)(  9, 44)( 10, 43)
( 11, 42)( 12, 41)( 13, 40)( 14, 39)( 15, 38)( 16, 37)( 17, 36)( 18, 35)
( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)( 26, 27)
( 51, 96)( 52, 95)( 53, 94)( 54, 93)( 55, 92)( 56, 91)( 57, 90)( 58, 89)
( 59, 88)( 60, 87)( 61, 86)( 62, 85)( 63, 84)( 64, 83)( 65, 82)( 66, 81)
( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 71, 76)( 72, 75)( 73, 74)( 98,143)
( 99,142)(100,141)(101,140)(102,139)(103,138)(104,137)(105,136)(106,135)
(107,134)(108,133)(109,132)(110,131)(111,130)(112,129)(113,128)(114,127)
(115,126)(116,125)(117,124)(118,123)(119,122)(120,121)(145,190)(146,189)
(147,188)(148,187)(149,186)(150,185)(151,184)(152,183)(153,182)(154,181)
(155,180)(156,179)(157,178)(158,177)(159,176)(160,175)(161,174)(162,173)
(163,172)(164,171)(165,170)(166,169)(167,168);
s2 := Sym(190)!(  3,  4)(  5, 49)(  6, 48)(  7, 47)(  8, 46)(  9, 45)( 10, 44)
( 11, 43)( 12, 42)( 13, 41)( 14, 40)( 15, 39)( 16, 38)( 17, 37)( 18, 36)
( 19, 35)( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)( 26, 28)
( 50, 51)( 52, 96)( 53, 95)( 54, 94)( 55, 93)( 56, 92)( 57, 91)( 58, 90)
( 59, 89)( 60, 88)( 61, 87)( 62, 86)( 63, 85)( 64, 84)( 65, 83)( 66, 82)
( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)( 73, 75)( 97,145)
( 98,144)( 99,190)(100,189)(101,188)(102,187)(103,186)(104,185)(105,184)
(106,183)(107,182)(108,181)(109,180)(110,179)(111,178)(112,177)(113,176)
(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,169)(121,168)
(122,167)(123,166)(124,165)(125,164)(126,163)(127,162)(128,161)(129,160)
(130,159)(131,158)(132,157)(133,156)(134,155)(135,154)(136,153)(137,152)
(138,151)(139,150)(140,149)(141,148)(142,147)(143,146);
s3 := Sym(190)!(  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)( 95,189)( 96,190);
poly := sub<Sym(190)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, 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 >;

to this polytope