Polytope of Type {12,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,24}*768f
if this polytope has a name.
Group : SmallGroup(768,1087808)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 16, 192, 32
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,12}*384a
   4-fold quotients : {6,12}*192a, {12,6}*192a
   8-fold quotients : {6,6}*96
   16-fold quotients : {3,6}*48, {6,3}*48
   24-fold quotients : {4,4}*32
   32-fold quotients : {3,3}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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