Polytope of Type {24,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*768f
if this polytope has a name.
Group : SmallGroup(768,1087808)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 32, 192, 16
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)( 25, 26)( 29, 32)( 30, 31)( 33, 42)( 34, 41)
( 35, 43)( 36, 44)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 51, 52)( 53, 55)
( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)( 62, 72)( 63, 69)
( 64, 70)( 73, 74)( 77, 80)( 78, 79)( 81, 90)( 82, 89)( 83, 91)( 84, 92)
( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 97,170)( 98,169)( 99,171)(100,172)
(101,176)(102,175)(103,174)(104,173)(105,186)(106,185)(107,187)(108,188)
(109,192)(110,191)(111,190)(112,189)(113,178)(114,177)(115,179)(116,180)
(117,184)(118,183)(119,182)(120,181)(121,145)(122,146)(123,148)(124,147)
(125,151)(126,152)(127,149)(128,150)(129,161)(130,162)(131,164)(132,163)
(133,167)(134,168)(135,165)(136,166)(137,153)(138,154)(139,156)(140,155)
(141,159)(142,160)(143,157)(144,158);;
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, 28)(  2, 27)(  3, 26)(  4, 25)(  5, 29)(  6, 30)(  7, 32)(  8, 31)
(  9, 44)( 10, 43)( 11, 42)( 12, 41)( 13, 45)( 14, 46)( 15, 48)( 16, 47)
( 17, 36)( 18, 35)( 19, 34)( 20, 33)( 21, 37)( 22, 38)( 23, 40)( 24, 39)
( 49, 75)( 50, 76)( 51, 73)( 52, 74)( 53, 78)( 54, 77)( 55, 79)( 56, 80)
( 57, 91)( 58, 92)( 59, 89)( 60, 90)( 61, 94)( 62, 93)( 63, 95)( 64, 96)
( 65, 83)( 66, 84)( 67, 81)( 68, 82)( 69, 86)( 70, 85)( 71, 87)( 72, 88)
( 97,100)( 98, 99)(103,104)(105,116)(106,115)(107,114)(108,113)(109,117)
(110,118)(111,120)(112,119)(121,124)(122,123)(127,128)(129,140)(130,139)
(131,138)(132,137)(133,141)(134,142)(135,144)(136,143)(145,147)(146,148)
(149,150)(153,163)(154,164)(155,161)(156,162)(157,166)(158,165)(159,167)
(160,168)(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*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*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)( 25, 26)( 29, 32)( 30, 31)( 33, 42)
( 34, 41)( 35, 43)( 36, 44)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 51, 52)
( 53, 55)( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)( 62, 72)
( 63, 69)( 64, 70)( 73, 74)( 77, 80)( 78, 79)( 81, 90)( 82, 89)( 83, 91)
( 84, 92)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 97,170)( 98,169)( 99,171)
(100,172)(101,176)(102,175)(103,174)(104,173)(105,186)(106,185)(107,187)
(108,188)(109,192)(110,191)(111,190)(112,189)(113,178)(114,177)(115,179)
(116,180)(117,184)(118,183)(119,182)(120,181)(121,145)(122,146)(123,148)
(124,147)(125,151)(126,152)(127,149)(128,150)(129,161)(130,162)(131,164)
(132,163)(133,167)(134,168)(135,165)(136,166)(137,153)(138,154)(139,156)
(140,155)(141,159)(142,160)(143,157)(144,158);
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, 28)(  2, 27)(  3, 26)(  4, 25)(  5, 29)(  6, 30)(  7, 32)
(  8, 31)(  9, 44)( 10, 43)( 11, 42)( 12, 41)( 13, 45)( 14, 46)( 15, 48)
( 16, 47)( 17, 36)( 18, 35)( 19, 34)( 20, 33)( 21, 37)( 22, 38)( 23, 40)
( 24, 39)( 49, 75)( 50, 76)( 51, 73)( 52, 74)( 53, 78)( 54, 77)( 55, 79)
( 56, 80)( 57, 91)( 58, 92)( 59, 89)( 60, 90)( 61, 94)( 62, 93)( 63, 95)
( 64, 96)( 65, 83)( 66, 84)( 67, 81)( 68, 82)( 69, 86)( 70, 85)( 71, 87)
( 72, 88)( 97,100)( 98, 99)(103,104)(105,116)(106,115)(107,114)(108,113)
(109,117)(110,118)(111,120)(112,119)(121,124)(122,123)(127,128)(129,140)
(130,139)(131,138)(132,137)(133,141)(134,142)(135,144)(136,143)(145,147)
(146,148)(149,150)(153,163)(154,164)(155,161)(156,162)(157,166)(158,165)
(159,167)(160,168)(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*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1 >;

References : None.
to this polytope