Polytope of Type {12,8}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope