Polytope of Type {8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*384d
if this polytope has a name.
Group : SmallGroup(384,5573)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 16, 96, 24
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,12,2} of size 768
Vertex Figure Of :
   {2,8,12} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,6}*192a
   8-fold quotients : {4,6}*48b
   16-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,12}*768k
   3-fold covers : {8,36}*1152d, {24,12}*1152h
   5-fold covers : {40,12}*1920d, {8,60}*1920d
Permutation Representation (GAP) :

s0 := (  1,113)(  2,114)(  3,115)(  4,116)(  5,117)(  6,118)(  7,119)(  8,120)
(  9,127)( 10,128)( 11,125)( 12,126)( 13,123)( 14,124)( 15,121)( 16,122)
( 17, 98)( 18, 97)( 19,100)( 20, 99)( 21,102)( 22,101)( 23,104)( 24,103)
( 25,112)( 26,111)( 27,110)( 28,109)( 29,108)( 30,107)( 31,106)( 32,105)
( 33,145)( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)( 40,152)
( 41,159)( 42,160)( 43,157)( 44,158)( 45,155)( 46,156)( 47,153)( 48,154)
( 49,130)( 50,129)( 51,132)( 52,131)( 53,134)( 54,133)( 55,136)( 56,135)
( 57,144)( 58,143)( 59,142)( 60,141)( 61,140)( 62,139)( 63,138)( 64,137)
( 65,177)( 66,178)( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)( 72,184)
( 73,191)( 74,192)( 75,189)( 76,190)( 77,187)( 78,188)( 79,185)( 80,186)
( 81,162)( 82,161)( 83,164)( 84,163)( 85,166)( 86,165)( 87,168)( 88,167)
( 89,176)( 90,175)( 91,174)( 92,173)( 93,172)( 94,171)( 95,170)( 96,169);;
s1 := (  5,  7)(  6,  8)(  9, 23)( 10, 24)( 11, 21)( 12, 22)( 13, 17)( 14, 18)
( 15, 19)( 16, 20)( 25, 28)( 26, 27)( 29, 30)( 31, 32)( 33, 65)( 34, 66)
( 35, 67)( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 87)( 42, 88)
( 43, 85)( 44, 86)( 45, 81)( 46, 82)( 47, 83)( 48, 84)( 49, 77)( 50, 78)
( 51, 79)( 52, 80)( 53, 75)( 54, 76)( 55, 73)( 56, 74)( 57, 92)( 58, 91)
( 59, 90)( 60, 89)( 61, 94)( 62, 93)( 63, 96)( 64, 95)( 97, 98)( 99,100)
(101,104)(102,103)(105,120)(106,119)(107,118)(108,117)(109,114)(110,113)
(111,116)(112,115)(121,123)(122,124)(129,162)(130,161)(131,164)(132,163)
(133,168)(134,167)(135,166)(136,165)(137,184)(138,183)(139,182)(140,181)
(141,178)(142,177)(143,180)(144,179)(145,174)(146,173)(147,176)(148,175)
(149,172)(150,171)(151,170)(152,169)(153,187)(154,188)(155,185)(156,186)
(157,189)(158,190)(159,191)(160,192);;
s2 := (  1,181)(  2,182)(  3,180)(  4,179)(  5,177)(  6,178)(  7,184)(  8,183)
(  9,170)( 10,169)( 11,175)( 12,176)( 13,174)( 14,173)( 15,171)( 16,172)
( 17,165)( 18,166)( 19,164)( 20,163)( 21,161)( 22,162)( 23,168)( 24,167)
( 25,190)( 26,189)( 27,187)( 28,188)( 29,186)( 30,185)( 31,191)( 32,192)
( 33,149)( 34,150)( 35,148)( 36,147)( 37,145)( 38,146)( 39,152)( 40,151)
( 41,138)( 42,137)( 43,143)( 44,144)( 45,142)( 46,141)( 47,139)( 48,140)
( 49,133)( 50,134)( 51,132)( 52,131)( 53,129)( 54,130)( 55,136)( 56,135)
( 57,158)( 58,157)( 59,155)( 60,156)( 61,154)( 62,153)( 63,159)( 64,160)
( 65,117)( 66,118)( 67,116)( 68,115)( 69,113)( 70,114)( 71,120)( 72,119)
( 73,106)( 74,105)( 75,111)( 76,112)( 77,110)( 78,109)( 79,107)( 80,108)
( 81,101)( 82,102)( 83,100)( 84, 99)( 85, 97)( 86, 98)( 87,104)( 88,103)
( 89,126)( 90,125)( 91,123)( 92,124)( 93,122)( 94,121)( 95,127)( 96,128);;
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, s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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)!(  1,113)(  2,114)(  3,115)(  4,116)(  5,117)(  6,118)(  7,119)
(  8,120)(  9,127)( 10,128)( 11,125)( 12,126)( 13,123)( 14,124)( 15,121)
( 16,122)( 17, 98)( 18, 97)( 19,100)( 20, 99)( 21,102)( 22,101)( 23,104)
( 24,103)( 25,112)( 26,111)( 27,110)( 28,109)( 29,108)( 30,107)( 31,106)
( 32,105)( 33,145)( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)
( 40,152)( 41,159)( 42,160)( 43,157)( 44,158)( 45,155)( 46,156)( 47,153)
( 48,154)( 49,130)( 50,129)( 51,132)( 52,131)( 53,134)( 54,133)( 55,136)
( 56,135)( 57,144)( 58,143)( 59,142)( 60,141)( 61,140)( 62,139)( 63,138)
( 64,137)( 65,177)( 66,178)( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)
( 72,184)( 73,191)( 74,192)( 75,189)( 76,190)( 77,187)( 78,188)( 79,185)
( 80,186)( 81,162)( 82,161)( 83,164)( 84,163)( 85,166)( 86,165)( 87,168)
( 88,167)( 89,176)( 90,175)( 91,174)( 92,173)( 93,172)( 94,171)( 95,170)
( 96,169);
s1 := Sym(192)!(  5,  7)(  6,  8)(  9, 23)( 10, 24)( 11, 21)( 12, 22)( 13, 17)
( 14, 18)( 15, 19)( 16, 20)( 25, 28)( 26, 27)( 29, 30)( 31, 32)( 33, 65)
( 34, 66)( 35, 67)( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 87)
( 42, 88)( 43, 85)( 44, 86)( 45, 81)( 46, 82)( 47, 83)( 48, 84)( 49, 77)
( 50, 78)( 51, 79)( 52, 80)( 53, 75)( 54, 76)( 55, 73)( 56, 74)( 57, 92)
( 58, 91)( 59, 90)( 60, 89)( 61, 94)( 62, 93)( 63, 96)( 64, 95)( 97, 98)
( 99,100)(101,104)(102,103)(105,120)(106,119)(107,118)(108,117)(109,114)
(110,113)(111,116)(112,115)(121,123)(122,124)(129,162)(130,161)(131,164)
(132,163)(133,168)(134,167)(135,166)(136,165)(137,184)(138,183)(139,182)
(140,181)(141,178)(142,177)(143,180)(144,179)(145,174)(146,173)(147,176)
(148,175)(149,172)(150,171)(151,170)(152,169)(153,187)(154,188)(155,185)
(156,186)(157,189)(158,190)(159,191)(160,192);
s2 := Sym(192)!(  1,181)(  2,182)(  3,180)(  4,179)(  5,177)(  6,178)(  7,184)
(  8,183)(  9,170)( 10,169)( 11,175)( 12,176)( 13,174)( 14,173)( 15,171)
( 16,172)( 17,165)( 18,166)( 19,164)( 20,163)( 21,161)( 22,162)( 23,168)
( 24,167)( 25,190)( 26,189)( 27,187)( 28,188)( 29,186)( 30,185)( 31,191)
( 32,192)( 33,149)( 34,150)( 35,148)( 36,147)( 37,145)( 38,146)( 39,152)
( 40,151)( 41,138)( 42,137)( 43,143)( 44,144)( 45,142)( 46,141)( 47,139)
( 48,140)( 49,133)( 50,134)( 51,132)( 52,131)( 53,129)( 54,130)( 55,136)
( 56,135)( 57,158)( 58,157)( 59,155)( 60,156)( 61,154)( 62,153)( 63,159)
( 64,160)( 65,117)( 66,118)( 67,116)( 68,115)( 69,113)( 70,114)( 71,120)
( 72,119)( 73,106)( 74,105)( 75,111)( 76,112)( 77,110)( 78,109)( 79,107)
( 80,108)( 81,101)( 82,102)( 83,100)( 84, 99)( 85, 97)( 86, 98)( 87,104)
( 88,103)( 89,126)( 90,125)( 91,123)( 92,124)( 93,122)( 94,121)( 95,127)
( 96,128);
poly := sub<Sym(192)|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, s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope