Polytope of Type {6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8}*768i
if this polytope has a name.
Group : SmallGroup(768,1086333)
Rank : 3
Schlafli Type : {6,8}
Number of vertices, edges, etc : 48, 192, 64
Order of s₀s₁s₂ : 6
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, {6,8}*192c
   8-fold quotients : {6,4}*96
   16-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,4}*24, {6,2}*24
   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 := (  1, 97)(  2, 98)(  3,100)(  4, 99)(  5,102)(  6,101)(  7,103)(  8,104)
(  9,112)( 10,111)( 11,109)( 12,110)( 13,107)( 14,108)( 15,106)( 16,105)
( 17,121)( 18,122)( 19,124)( 20,123)( 21,126)( 22,125)( 23,127)( 24,128)
( 25,113)( 26,114)( 27,116)( 28,115)( 29,118)( 30,117)( 31,119)( 32,120)
( 33,161)( 34,162)( 35,164)( 36,163)( 37,166)( 38,165)( 39,167)( 40,168)
( 41,176)( 42,175)( 43,173)( 44,174)( 45,171)( 46,172)( 47,170)( 48,169)
( 49,185)( 50,186)( 51,188)( 52,187)( 53,190)( 54,189)( 55,191)( 56,192)
( 57,177)( 58,178)( 59,180)( 60,179)( 61,182)( 62,181)( 63,183)( 64,184)
( 65,129)( 66,130)( 67,132)( 68,131)( 69,134)( 70,133)( 71,135)( 72,136)
( 73,144)( 74,143)( 75,141)( 76,142)( 77,139)( 78,140)( 79,138)( 80,137)
( 81,153)( 82,154)( 83,156)( 84,155)( 85,158)( 86,157)( 87,159)( 88,160)
( 89,145)( 90,146)( 91,148)( 92,147)( 93,150)( 94,149)( 95,151)( 96,152);;
s1 := (  1, 65)(  2, 67)(  3, 66)(  4, 68)(  5, 72)(  6, 70)(  7, 71)(  8, 69)
(  9, 88)( 10, 86)( 11, 87)( 12, 85)( 13, 81)( 14, 83)( 15, 82)( 16, 84)
( 17, 77)( 18, 79)( 19, 78)( 20, 80)( 21, 76)( 22, 74)( 23, 75)( 24, 73)
( 25, 94)( 26, 96)( 27, 93)( 28, 95)( 29, 91)( 30, 89)( 31, 92)( 32, 90)
( 34, 35)( 37, 40)( 41, 56)( 42, 54)( 43, 55)( 44, 53)( 45, 49)( 46, 51)
( 47, 50)( 48, 52)( 57, 62)( 58, 64)( 59, 61)( 60, 63)( 97,161)( 98,163)
( 99,162)(100,164)(101,168)(102,166)(103,167)(104,165)(105,184)(106,182)
(107,183)(108,181)(109,177)(110,179)(111,178)(112,180)(113,173)(114,175)
(115,174)(116,176)(117,172)(118,170)(119,171)(120,169)(121,190)(122,192)
(123,189)(124,191)(125,187)(126,185)(127,188)(128,186)(130,131)(133,136)
(137,152)(138,150)(139,151)(140,149)(141,145)(142,147)(143,146)(144,148)
(153,158)(154,160)(155,157)(156,159);;
s2 := (  1,108)(  2,107)(  3,106)(  4,105)(  5,112)(  6,111)(  7,110)(  8,109)
(  9,102)( 10,101)( 11,104)( 12,103)( 13, 98)( 14, 97)( 15,100)( 16, 99)
( 17,122)( 18,121)( 19,124)( 20,123)( 21,126)( 22,125)( 23,128)( 24,127)
( 25,120)( 26,119)( 27,118)( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)
( 33,140)( 34,139)( 35,138)( 36,137)( 37,144)( 38,143)( 39,142)( 40,141)
( 41,134)( 42,133)( 43,136)( 44,135)( 45,130)( 46,129)( 47,132)( 48,131)
( 49,154)( 50,153)( 51,156)( 52,155)( 53,158)( 54,157)( 55,160)( 56,159)
( 57,152)( 58,151)( 59,150)( 60,149)( 61,148)( 62,147)( 63,146)( 64,145)
( 65,172)( 66,171)( 67,170)( 68,169)( 69,176)( 70,175)( 71,174)( 72,173)
( 73,166)( 74,165)( 75,168)( 76,167)( 77,162)( 78,161)( 79,164)( 80,163)
( 81,186)( 82,185)( 83,188)( 84,187)( 85,190)( 86,189)( 87,192)( 88,191)
( 89,184)( 90,183)( 91,182)( 92,181)( 93,180)( 94,179)( 95,178)( 96,177);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope