Polytope of Type {8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*768w
if this polytope has a name.
Group : SmallGroup(768,1087796)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 32, 192, 48
Order of s0s1s2 : 24
Order of s0s1s2s1 : 4
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 : {4,12}*384d
   4-fold quotients : {8,12}*192b, {4,12}*192b, {4,6}*192b, {4,12}*192c
   8-fold quotients : {4,12}*96a, {4,12}*96b, {4,12}*96c, {4,6}*96
   12-fold quotients : {8,4}*64b
   16-fold quotients : {2,12}*48, {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
   24-fold quotients : {4,4}*32
   32-fold quotients : {4,3}*24, {2,6}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   64-fold quotients : {2,3}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,  4)(  2,  3)(  5,  8)(  6,  7)(  9, 12)( 10, 11)( 13, 16)( 14, 15)
( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 25, 40)( 26, 39)( 27, 38)( 28, 37)
( 29, 44)( 30, 43)( 31, 42)( 32, 41)( 33, 48)( 34, 47)( 35, 46)( 36, 45)
( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 68)( 54, 67)( 55, 66)( 56, 65)
( 57, 72)( 58, 71)( 59, 70)( 60, 69)( 73, 76)( 74, 75)( 77, 80)( 78, 79)
( 81, 84)( 82, 83)( 85, 88)( 86, 87)( 89, 92)( 90, 91)( 93, 96)( 94, 95)
( 97,148)( 98,147)( 99,146)(100,145)(101,152)(102,151)(103,150)(104,149)
(105,156)(106,155)(107,154)(108,153)(109,160)(110,159)(111,158)(112,157)
(113,164)(114,163)(115,162)(116,161)(117,168)(118,167)(119,166)(120,165)
(121,184)(122,183)(123,182)(124,181)(125,188)(126,187)(127,186)(128,185)
(129,192)(130,191)(131,190)(132,189)(133,172)(134,171)(135,170)(136,169)
(137,176)(138,175)(139,174)(140,173)(141,180)(142,179)(143,178)(144,177);;
s1 := (  1,121)(  2,122)(  3,124)(  4,123)(  5,129)(  6,130)(  7,132)(  8,131)
(  9,125)( 10,126)( 11,128)( 12,127)( 13,133)( 14,134)( 15,136)( 16,135)
( 17,141)( 18,142)( 19,144)( 20,143)( 21,137)( 22,138)( 23,140)( 24,139)
( 25, 97)( 26, 98)( 27,100)( 28, 99)( 29,105)( 30,106)( 31,108)( 32,107)
( 33,101)( 34,102)( 35,104)( 36,103)( 37,109)( 38,110)( 39,112)( 40,111)
( 41,117)( 42,118)( 43,120)( 44,119)( 45,113)( 46,114)( 47,116)( 48,115)
( 49,181)( 50,182)( 51,184)( 52,183)( 53,189)( 54,190)( 55,192)( 56,191)
( 57,185)( 58,186)( 59,188)( 60,187)( 61,169)( 62,170)( 63,172)( 64,171)
( 65,177)( 66,178)( 67,180)( 68,179)( 69,173)( 70,174)( 71,176)( 72,175)
( 73,157)( 74,158)( 75,160)( 76,159)( 77,165)( 78,166)( 79,168)( 80,167)
( 81,161)( 82,162)( 83,164)( 84,163)( 85,145)( 86,146)( 87,148)( 88,147)
( 89,153)( 90,154)( 91,156)( 92,155)( 93,149)( 94,150)( 95,152)( 96,151);;
s2 := (  1,  9)(  2, 11)(  3, 10)(  4, 12)(  6,  7)( 13, 21)( 14, 23)( 15, 22)
( 16, 24)( 18, 19)( 25, 33)( 26, 35)( 27, 34)( 28, 36)( 30, 31)( 37, 45)
( 38, 47)( 39, 46)( 40, 48)( 42, 43)( 49, 69)( 50, 71)( 51, 70)( 52, 72)
( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 61)( 58, 63)( 59, 62)( 60, 64)
( 73, 93)( 74, 95)( 75, 94)( 76, 96)( 77, 89)( 78, 91)( 79, 90)( 80, 92)
( 81, 85)( 82, 87)( 83, 86)( 84, 88)( 97,129)( 98,131)( 99,130)(100,132)
(101,125)(102,127)(103,126)(104,128)(105,121)(106,123)(107,122)(108,124)
(109,141)(110,143)(111,142)(112,144)(113,137)(114,139)(115,138)(116,140)
(117,133)(118,135)(119,134)(120,136)(145,189)(146,191)(147,190)(148,192)
(149,185)(150,187)(151,186)(152,188)(153,181)(154,183)(155,182)(156,184)
(157,177)(158,179)(159,178)(160,180)(161,173)(162,175)(163,174)(164,176)
(165,169)(166,171)(167,170)(168,172);;
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*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*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)!(  1,  4)(  2,  3)(  5,  8)(  6,  7)(  9, 12)( 10, 11)( 13, 16)
( 14, 15)( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 25, 40)( 26, 39)( 27, 38)
( 28, 37)( 29, 44)( 30, 43)( 31, 42)( 32, 41)( 33, 48)( 34, 47)( 35, 46)
( 36, 45)( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 68)( 54, 67)( 55, 66)
( 56, 65)( 57, 72)( 58, 71)( 59, 70)( 60, 69)( 73, 76)( 74, 75)( 77, 80)
( 78, 79)( 81, 84)( 82, 83)( 85, 88)( 86, 87)( 89, 92)( 90, 91)( 93, 96)
( 94, 95)( 97,148)( 98,147)( 99,146)(100,145)(101,152)(102,151)(103,150)
(104,149)(105,156)(106,155)(107,154)(108,153)(109,160)(110,159)(111,158)
(112,157)(113,164)(114,163)(115,162)(116,161)(117,168)(118,167)(119,166)
(120,165)(121,184)(122,183)(123,182)(124,181)(125,188)(126,187)(127,186)
(128,185)(129,192)(130,191)(131,190)(132,189)(133,172)(134,171)(135,170)
(136,169)(137,176)(138,175)(139,174)(140,173)(141,180)(142,179)(143,178)
(144,177);
s1 := Sym(192)!(  1,121)(  2,122)(  3,124)(  4,123)(  5,129)(  6,130)(  7,132)
(  8,131)(  9,125)( 10,126)( 11,128)( 12,127)( 13,133)( 14,134)( 15,136)
( 16,135)( 17,141)( 18,142)( 19,144)( 20,143)( 21,137)( 22,138)( 23,140)
( 24,139)( 25, 97)( 26, 98)( 27,100)( 28, 99)( 29,105)( 30,106)( 31,108)
( 32,107)( 33,101)( 34,102)( 35,104)( 36,103)( 37,109)( 38,110)( 39,112)
( 40,111)( 41,117)( 42,118)( 43,120)( 44,119)( 45,113)( 46,114)( 47,116)
( 48,115)( 49,181)( 50,182)( 51,184)( 52,183)( 53,189)( 54,190)( 55,192)
( 56,191)( 57,185)( 58,186)( 59,188)( 60,187)( 61,169)( 62,170)( 63,172)
( 64,171)( 65,177)( 66,178)( 67,180)( 68,179)( 69,173)( 70,174)( 71,176)
( 72,175)( 73,157)( 74,158)( 75,160)( 76,159)( 77,165)( 78,166)( 79,168)
( 80,167)( 81,161)( 82,162)( 83,164)( 84,163)( 85,145)( 86,146)( 87,148)
( 88,147)( 89,153)( 90,154)( 91,156)( 92,155)( 93,149)( 94,150)( 95,152)
( 96,151);
s2 := Sym(192)!(  1,  9)(  2, 11)(  3, 10)(  4, 12)(  6,  7)( 13, 21)( 14, 23)
( 15, 22)( 16, 24)( 18, 19)( 25, 33)( 26, 35)( 27, 34)( 28, 36)( 30, 31)
( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 42, 43)( 49, 69)( 50, 71)( 51, 70)
( 52, 72)( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 61)( 58, 63)( 59, 62)
( 60, 64)( 73, 93)( 74, 95)( 75, 94)( 76, 96)( 77, 89)( 78, 91)( 79, 90)
( 80, 92)( 81, 85)( 82, 87)( 83, 86)( 84, 88)( 97,129)( 98,131)( 99,130)
(100,132)(101,125)(102,127)(103,126)(104,128)(105,121)(106,123)(107,122)
(108,124)(109,141)(110,143)(111,142)(112,144)(113,137)(114,139)(115,138)
(116,140)(117,133)(118,135)(119,134)(120,136)(145,189)(146,191)(147,190)
(148,192)(149,185)(150,187)(151,186)(152,188)(153,181)(154,183)(155,182)
(156,184)(157,177)(158,179)(159,178)(160,180)(161,173)(162,175)(163,174)
(164,176)(165,169)(166,171)(167,170)(168,172);
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*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope