Polytope of Type {6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8}*768l
if this polytope has a name.
Group : SmallGroup(768,1088009)
Rank : 3
Schlafli Type : {6,8}
Number of vertices, edges, etc : 48, 192, 64
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}*384d
   4-fold quotients : {6,8}*192a, {6,4}*192b
   8-fold quotients : {6,4}*96
   16-fold quotients : {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,4}*24, {6,2}*24
   48-fold quotients : {2,4}*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)( 99,100)(101,102)(105,109)(106,110)
(107,112)(108,111)(113,129)(114,130)(115,132)(116,131)(117,134)(118,133)
(119,135)(120,136)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)
(127,140)(128,139)(147,148)(149,150)(153,157)(154,158)(155,160)(156,159)
(161,177)(162,178)(163,180)(164,179)(165,182)(166,181)(167,183)(168,184)
(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187);;
s1 := (  1, 33)(  2, 35)(  3, 34)(  4, 36)(  5, 42)(  6, 44)(  7, 41)(  8, 43)
(  9, 39)( 10, 37)( 11, 40)( 12, 38)( 13, 48)( 14, 46)( 15, 47)( 16, 45)
( 18, 19)( 21, 26)( 22, 28)( 23, 25)( 24, 27)( 29, 32)( 49, 81)( 50, 83)
( 51, 82)( 52, 84)( 53, 90)( 54, 92)( 55, 89)( 56, 91)( 57, 87)( 58, 85)
( 59, 88)( 60, 86)( 61, 96)( 62, 94)( 63, 95)( 64, 93)( 66, 67)( 69, 74)
( 70, 76)( 71, 73)( 72, 75)( 77, 80)( 97,177)( 98,179)( 99,178)(100,180)
(101,186)(102,188)(103,185)(104,187)(105,183)(106,181)(107,184)(108,182)
(109,192)(110,190)(111,191)(112,189)(113,161)(114,163)(115,162)(116,164)
(117,170)(118,172)(119,169)(120,171)(121,167)(122,165)(123,168)(124,166)
(125,176)(126,174)(127,175)(128,173)(129,145)(130,147)(131,146)(132,148)
(133,154)(134,156)(135,153)(136,155)(137,151)(138,149)(139,152)(140,150)
(141,160)(142,158)(143,159)(144,157);;
s2 := (  1,103)(  2,104)(  3,101)(  4,102)(  5, 99)(  6,100)(  7, 97)(  8, 98)
(  9,109)( 10,110)( 11,111)( 12,112)( 13,105)( 14,106)( 15,107)( 16,108)
( 17,119)( 18,120)( 19,117)( 20,118)( 21,115)( 22,116)( 23,113)( 24,114)
( 25,125)( 26,126)( 27,127)( 28,128)( 29,121)( 30,122)( 31,123)( 32,124)
( 33,135)( 34,136)( 35,133)( 36,134)( 37,131)( 38,132)( 39,129)( 40,130)
( 41,141)( 42,142)( 43,143)( 44,144)( 45,137)( 46,138)( 47,139)( 48,140)
( 49,151)( 50,152)( 51,149)( 52,150)( 53,147)( 54,148)( 55,145)( 56,146)
( 57,157)( 58,158)( 59,159)( 60,160)( 61,153)( 62,154)( 63,155)( 64,156)
( 65,167)( 66,168)( 67,165)( 68,166)( 69,163)( 70,164)( 71,161)( 72,162)
( 73,173)( 74,174)( 75,175)( 76,176)( 77,169)( 78,170)( 79,171)( 80,172)
( 81,183)( 82,184)( 83,181)( 84,182)( 85,179)( 86,180)( 87,177)( 88,178)
( 89,189)( 90,190)( 91,191)( 92,192)( 93,185)( 94,186)( 95,187)( 96,188);;
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, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*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)( 99,100)(101,102)(105,109)
(106,110)(107,112)(108,111)(113,129)(114,130)(115,132)(116,131)(117,134)
(118,133)(119,135)(120,136)(121,141)(122,142)(123,144)(124,143)(125,137)
(126,138)(127,140)(128,139)(147,148)(149,150)(153,157)(154,158)(155,160)
(156,159)(161,177)(162,178)(163,180)(164,179)(165,182)(166,181)(167,183)
(168,184)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)
(176,187);
s1 := Sym(192)!(  1, 33)(  2, 35)(  3, 34)(  4, 36)(  5, 42)(  6, 44)(  7, 41)
(  8, 43)(  9, 39)( 10, 37)( 11, 40)( 12, 38)( 13, 48)( 14, 46)( 15, 47)
( 16, 45)( 18, 19)( 21, 26)( 22, 28)( 23, 25)( 24, 27)( 29, 32)( 49, 81)
( 50, 83)( 51, 82)( 52, 84)( 53, 90)( 54, 92)( 55, 89)( 56, 91)( 57, 87)
( 58, 85)( 59, 88)( 60, 86)( 61, 96)( 62, 94)( 63, 95)( 64, 93)( 66, 67)
( 69, 74)( 70, 76)( 71, 73)( 72, 75)( 77, 80)( 97,177)( 98,179)( 99,178)
(100,180)(101,186)(102,188)(103,185)(104,187)(105,183)(106,181)(107,184)
(108,182)(109,192)(110,190)(111,191)(112,189)(113,161)(114,163)(115,162)
(116,164)(117,170)(118,172)(119,169)(120,171)(121,167)(122,165)(123,168)
(124,166)(125,176)(126,174)(127,175)(128,173)(129,145)(130,147)(131,146)
(132,148)(133,154)(134,156)(135,153)(136,155)(137,151)(138,149)(139,152)
(140,150)(141,160)(142,158)(143,159)(144,157);
s2 := Sym(192)!(  1,103)(  2,104)(  3,101)(  4,102)(  5, 99)(  6,100)(  7, 97)
(  8, 98)(  9,109)( 10,110)( 11,111)( 12,112)( 13,105)( 14,106)( 15,107)
( 16,108)( 17,119)( 18,120)( 19,117)( 20,118)( 21,115)( 22,116)( 23,113)
( 24,114)( 25,125)( 26,126)( 27,127)( 28,128)( 29,121)( 30,122)( 31,123)
( 32,124)( 33,135)( 34,136)( 35,133)( 36,134)( 37,131)( 38,132)( 39,129)
( 40,130)( 41,141)( 42,142)( 43,143)( 44,144)( 45,137)( 46,138)( 47,139)
( 48,140)( 49,151)( 50,152)( 51,149)( 52,150)( 53,147)( 54,148)( 55,145)
( 56,146)( 57,157)( 58,158)( 59,159)( 60,160)( 61,153)( 62,154)( 63,155)
( 64,156)( 65,167)( 66,168)( 67,165)( 68,166)( 69,163)( 70,164)( 71,161)
( 72,162)( 73,173)( 74,174)( 75,175)( 76,176)( 77,169)( 78,170)( 79,171)
( 80,172)( 81,183)( 82,184)( 83,181)( 84,182)( 85,179)( 86,180)( 87,177)
( 88,178)( 89,189)( 90,190)( 91,191)( 92,192)( 93,185)( 94,186)( 95,187)
( 96,188);
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, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 >;

References : None.
to this polytope