Polytope of Type {12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*768r
if this polytope has a name.
Group : SmallGroup(768,1087633)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 48, 192, 32
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 8
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 : {6,8}*384e
   4-fold quotients : {3,8}*192, {12,4}*192b
   8-fold quotients : {12,4}*96b, {12,4}*96c, {6,4}*96
   16-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,4}*24, {6,2}*24
   48-fold quotients : {4,2}*16
   64-fold quotients : {3,2}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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