Polytope of Type {8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*768r
if this polytope has a name.
Group : SmallGroup(768,1087633)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 32, 192, 48
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,6}*384d
   4-fold quotients : {8,6}*192a, {4,12}*192b
   8-fold quotients : {4,12}*96b, {4,12}*96c, {4,6}*96
   16-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {4,3}*24, {2,6}*24
   48-fold quotients : {2,4}*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, 16)(  2, 15)(  3, 14)(  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)
( 17, 32)( 18, 31)( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 24, 25)
( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 40, 41)
( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58)( 56, 57)
( 65, 80)( 66, 79)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)
( 81, 96)( 82, 95)( 83, 94)( 84, 93)( 85, 92)( 86, 91)( 87, 90)( 88, 89)
( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)(104,105)
(113,128)(114,127)(115,126)(116,125)(117,124)(118,123)(119,122)(120,121)
(129,144)(130,143)(131,142)(132,141)(133,140)(134,139)(135,138)(136,137)
(145,160)(146,159)(147,158)(148,157)(149,156)(150,155)(151,154)(152,153)
(161,176)(162,175)(163,174)(164,173)(165,172)(166,171)(167,170)(168,169)
(177,192)(178,191)(179,190)(180,189)(181,188)(182,187)(183,186)(184,185);;
s1 := (  3,  4)(  5,  6)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 38)( 22, 37)( 23, 39)( 24, 40)( 25, 45)( 26, 46)
( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 51, 52)( 53, 54)
( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 65, 81)( 66, 82)( 67, 84)( 68, 83)
( 69, 86)( 70, 85)( 71, 87)( 72, 88)( 73, 93)( 74, 94)( 75, 96)( 76, 95)
( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 97,145)( 98,146)( 99,148)(100,147)
(101,150)(102,149)(103,151)(104,152)(105,157)(106,158)(107,160)(108,159)
(109,153)(110,154)(111,156)(112,155)(113,177)(114,178)(115,180)(116,179)
(117,182)(118,181)(119,183)(120,184)(121,189)(122,190)(123,192)(124,191)
(125,185)(126,186)(127,188)(128,187)(129,161)(130,162)(131,164)(132,163)
(133,166)(134,165)(135,167)(136,168)(137,173)(138,174)(139,176)(140,175)
(141,169)(142,170)(143,172)(144,171);;
s2 := (  1,192)(  2,190)(  3,191)(  4,189)(  5,181)(  6,183)(  7,182)(  8,184)
(  9,185)( 10,187)( 11,186)( 12,188)( 13,180)( 14,178)( 15,179)( 16,177)
( 17,176)( 18,174)( 19,175)( 20,173)( 21,165)( 22,167)( 23,166)( 24,168)
( 25,169)( 26,171)( 27,170)( 28,172)( 29,164)( 30,162)( 31,163)( 32,161)
( 33,160)( 34,158)( 35,159)( 36,157)( 37,149)( 38,151)( 39,150)( 40,152)
( 41,153)( 42,155)( 43,154)( 44,156)( 45,148)( 46,146)( 47,147)( 48,145)
( 49,144)( 50,142)( 51,143)( 52,141)( 53,133)( 54,135)( 55,134)( 56,136)
( 57,137)( 58,139)( 59,138)( 60,140)( 61,132)( 62,130)( 63,131)( 64,129)
( 65,128)( 66,126)( 67,127)( 68,125)( 69,117)( 70,119)( 71,118)( 72,120)
( 73,121)( 74,123)( 75,122)( 76,124)( 77,116)( 78,114)( 79,115)( 80,113)
( 81,112)( 82,110)( 83,111)( 84,109)( 85,101)( 86,103)( 87,102)( 88,104)
( 89,105)( 90,107)( 91,106)( 92,108)( 93,100)( 94, 98)( 95, 99)( 96, 97);;
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*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*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, 16)(  2, 15)(  3, 14)(  4, 13)(  5, 12)(  6, 11)(  7, 10)
(  8,  9)( 17, 32)( 18, 31)( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)
( 24, 25)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)
( 40, 41)( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58)
( 56, 57)( 65, 80)( 66, 79)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)
( 72, 73)( 81, 96)( 82, 95)( 83, 94)( 84, 93)( 85, 92)( 86, 91)( 87, 90)
( 88, 89)( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)
(104,105)(113,128)(114,127)(115,126)(116,125)(117,124)(118,123)(119,122)
(120,121)(129,144)(130,143)(131,142)(132,141)(133,140)(134,139)(135,138)
(136,137)(145,160)(146,159)(147,158)(148,157)(149,156)(150,155)(151,154)
(152,153)(161,176)(162,175)(163,174)(164,173)(165,172)(166,171)(167,170)
(168,169)(177,192)(178,191)(179,190)(180,189)(181,188)(182,187)(183,186)
(184,185);
s1 := Sym(192)!(  3,  4)(  5,  6)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)
( 18, 34)( 19, 36)( 20, 35)( 21, 38)( 22, 37)( 23, 39)( 24, 40)( 25, 45)
( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 51, 52)
( 53, 54)( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 65, 81)( 66, 82)( 67, 84)
( 68, 83)( 69, 86)( 70, 85)( 71, 87)( 72, 88)( 73, 93)( 74, 94)( 75, 96)
( 76, 95)( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 97,145)( 98,146)( 99,148)
(100,147)(101,150)(102,149)(103,151)(104,152)(105,157)(106,158)(107,160)
(108,159)(109,153)(110,154)(111,156)(112,155)(113,177)(114,178)(115,180)
(116,179)(117,182)(118,181)(119,183)(120,184)(121,189)(122,190)(123,192)
(124,191)(125,185)(126,186)(127,188)(128,187)(129,161)(130,162)(131,164)
(132,163)(133,166)(134,165)(135,167)(136,168)(137,173)(138,174)(139,176)
(140,175)(141,169)(142,170)(143,172)(144,171);
s2 := Sym(192)!(  1,192)(  2,190)(  3,191)(  4,189)(  5,181)(  6,183)(  7,182)
(  8,184)(  9,185)( 10,187)( 11,186)( 12,188)( 13,180)( 14,178)( 15,179)
( 16,177)( 17,176)( 18,174)( 19,175)( 20,173)( 21,165)( 22,167)( 23,166)
( 24,168)( 25,169)( 26,171)( 27,170)( 28,172)( 29,164)( 30,162)( 31,163)
( 32,161)( 33,160)( 34,158)( 35,159)( 36,157)( 37,149)( 38,151)( 39,150)
( 40,152)( 41,153)( 42,155)( 43,154)( 44,156)( 45,148)( 46,146)( 47,147)
( 48,145)( 49,144)( 50,142)( 51,143)( 52,141)( 53,133)( 54,135)( 55,134)
( 56,136)( 57,137)( 58,139)( 59,138)( 60,140)( 61,132)( 62,130)( 63,131)
( 64,129)( 65,128)( 66,126)( 67,127)( 68,125)( 69,117)( 70,119)( 71,118)
( 72,120)( 73,121)( 74,123)( 75,122)( 76,124)( 77,116)( 78,114)( 79,115)
( 80,113)( 81,112)( 82,110)( 83,111)( 84,109)( 85,101)( 86,103)( 87,102)
( 88,104)( 89,105)( 90,107)( 91,106)( 92,108)( 93,100)( 94, 98)( 95, 99)
( 96, 97);
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*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*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