Polytope of Type {192}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {192}*384
Also Known As : 192-gon, {192}. if this polytope has another name.
Group : SmallGroup(384,9)
Rank : 2
Schlafli Type : {192}
Number of vertices, edges, etc : 192, 192
Order of s₀s₁ : 192
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {192,2} of size 768
Vertex Figure Of :
   {2,192} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {96}*192
   3-fold quotients : {64}*128
   4-fold quotients : {48}*96
   6-fold quotients : {32}*64
   8-fold quotients : {24}*48
   12-fold quotients : {16}*32
   16-fold quotients : {12}*24
   24-fold quotients : {8}*16
   32-fold quotients : {6}*12
   48-fold quotients : {4}*8
   64-fold quotients : {3}*6
   96-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {384}*768
   3-fold covers : {576}*1152
   5-fold covers : {960}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope