Polytope of Type {8,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,2}*768a
if this polytope has a name.
Group : SmallGroup(768,1086301)
Rank : 4
Schlafli Type : {8,6,2}
Number of vertices, edges, etc : 32, 96, 24, 2
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
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 : {8,3,2}*384
   8-fold quotients : {4,3,2}*96
   16-fold quotients : {4,3,2}*48
   32-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,113)(  2,114)(  3,115)(  4,116)(  5,117)(  6,118)(  7,119)(  8,120)
(  9,127)( 10,128)( 11,125)( 12,126)( 13,123)( 14,124)( 15,121)( 16,122)
( 17, 98)( 18, 97)( 19,100)( 20, 99)( 21,102)( 22,101)( 23,104)( 24,103)
( 25,112)( 26,111)( 27,110)( 28,109)( 29,108)( 30,107)( 31,106)( 32,105)
( 33,145)( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)( 40,152)
( 41,159)( 42,160)( 43,157)( 44,158)( 45,155)( 46,156)( 47,153)( 48,154)
( 49,130)( 50,129)( 51,132)( 52,131)( 53,134)( 54,133)( 55,136)( 56,135)
( 57,144)( 58,143)( 59,142)( 60,141)( 61,140)( 62,139)( 63,138)( 64,137)
( 65,177)( 66,178)( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)( 72,184)
( 73,191)( 74,192)( 75,189)( 76,190)( 77,187)( 78,188)( 79,185)( 80,186)
( 81,162)( 82,161)( 83,164)( 84,163)( 85,166)( 86,165)( 87,168)( 88,167)
( 89,176)( 90,175)( 91,174)( 92,173)( 93,172)( 94,171)( 95,170)( 96,169);;
s1 := (  5,  7)(  6,  8)(  9, 23)( 10, 24)( 11, 21)( 12, 22)( 13, 17)( 14, 18)
( 15, 19)( 16, 20)( 25, 28)( 26, 27)( 29, 30)( 31, 32)( 33, 65)( 34, 66)
( 35, 67)( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 87)( 42, 88)
( 43, 85)( 44, 86)( 45, 81)( 46, 82)( 47, 83)( 48, 84)( 49, 77)( 50, 78)
( 51, 79)( 52, 80)( 53, 75)( 54, 76)( 55, 73)( 56, 74)( 57, 92)( 58, 91)
( 59, 90)( 60, 89)( 61, 94)( 62, 93)( 63, 96)( 64, 95)( 97, 98)( 99,100)
(101,104)(102,103)(105,120)(106,119)(107,118)(108,117)(109,114)(110,113)
(111,116)(112,115)(121,123)(122,124)(129,162)(130,161)(131,164)(132,163)
(133,168)(134,167)(135,166)(136,165)(137,184)(138,183)(139,182)(140,181)
(141,178)(142,177)(143,180)(144,179)(145,174)(146,173)(147,176)(148,175)
(149,172)(150,171)(151,170)(152,169)(153,187)(154,188)(155,185)(156,186)
(157,189)(158,190)(159,191)(160,192);;
s2 := (  1, 69)(  2, 70)(  3, 68)(  4, 67)(  5, 65)(  6, 66)(  7, 72)(  8, 71)
(  9, 95)( 10, 96)( 11, 90)( 12, 89)( 13, 91)( 14, 92)( 15, 94)( 16, 93)
( 17, 86)( 18, 85)( 19, 83)( 20, 84)( 21, 82)( 22, 81)( 23, 87)( 24, 88)
( 25, 76)( 26, 75)( 27, 77)( 28, 78)( 29, 80)( 30, 79)( 31, 73)( 32, 74)
( 33, 37)( 34, 38)( 35, 36)( 39, 40)( 41, 63)( 42, 64)( 43, 58)( 44, 57)
( 45, 59)( 46, 60)( 47, 62)( 48, 61)( 49, 54)( 50, 53)( 97,166)( 98,165)
( 99,163)(100,164)(101,162)(102,161)(103,167)(104,168)(105,192)(106,191)
(107,185)(108,186)(109,188)(110,187)(111,189)(112,190)(113,181)(114,182)
(115,180)(116,179)(117,177)(118,178)(119,184)(120,183)(121,171)(122,172)
(123,174)(124,173)(125,175)(126,176)(127,170)(128,169)(129,134)(130,133)
(137,160)(138,159)(139,153)(140,154)(141,156)(142,155)(143,157)(144,158)
(145,149)(146,150)(147,148)(151,152);;
s3 := (193,194);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(194)!(  1,113)(  2,114)(  3,115)(  4,116)(  5,117)(  6,118)(  7,119)
(  8,120)(  9,127)( 10,128)( 11,125)( 12,126)( 13,123)( 14,124)( 15,121)
( 16,122)( 17, 98)( 18, 97)( 19,100)( 20, 99)( 21,102)( 22,101)( 23,104)
( 24,103)( 25,112)( 26,111)( 27,110)( 28,109)( 29,108)( 30,107)( 31,106)
( 32,105)( 33,145)( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)
( 40,152)( 41,159)( 42,160)( 43,157)( 44,158)( 45,155)( 46,156)( 47,153)
( 48,154)( 49,130)( 50,129)( 51,132)( 52,131)( 53,134)( 54,133)( 55,136)
( 56,135)( 57,144)( 58,143)( 59,142)( 60,141)( 61,140)( 62,139)( 63,138)
( 64,137)( 65,177)( 66,178)( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)
( 72,184)( 73,191)( 74,192)( 75,189)( 76,190)( 77,187)( 78,188)( 79,185)
( 80,186)( 81,162)( 82,161)( 83,164)( 84,163)( 85,166)( 86,165)( 87,168)
( 88,167)( 89,176)( 90,175)( 91,174)( 92,173)( 93,172)( 94,171)( 95,170)
( 96,169);
s1 := Sym(194)!(  5,  7)(  6,  8)(  9, 23)( 10, 24)( 11, 21)( 12, 22)( 13, 17)
( 14, 18)( 15, 19)( 16, 20)( 25, 28)( 26, 27)( 29, 30)( 31, 32)( 33, 65)
( 34, 66)( 35, 67)( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 87)
( 42, 88)( 43, 85)( 44, 86)( 45, 81)( 46, 82)( 47, 83)( 48, 84)( 49, 77)
( 50, 78)( 51, 79)( 52, 80)( 53, 75)( 54, 76)( 55, 73)( 56, 74)( 57, 92)
( 58, 91)( 59, 90)( 60, 89)( 61, 94)( 62, 93)( 63, 96)( 64, 95)( 97, 98)
( 99,100)(101,104)(102,103)(105,120)(106,119)(107,118)(108,117)(109,114)
(110,113)(111,116)(112,115)(121,123)(122,124)(129,162)(130,161)(131,164)
(132,163)(133,168)(134,167)(135,166)(136,165)(137,184)(138,183)(139,182)
(140,181)(141,178)(142,177)(143,180)(144,179)(145,174)(146,173)(147,176)
(148,175)(149,172)(150,171)(151,170)(152,169)(153,187)(154,188)(155,185)
(156,186)(157,189)(158,190)(159,191)(160,192);
s2 := Sym(194)!(  1, 69)(  2, 70)(  3, 68)(  4, 67)(  5, 65)(  6, 66)(  7, 72)
(  8, 71)(  9, 95)( 10, 96)( 11, 90)( 12, 89)( 13, 91)( 14, 92)( 15, 94)
( 16, 93)( 17, 86)( 18, 85)( 19, 83)( 20, 84)( 21, 82)( 22, 81)( 23, 87)
( 24, 88)( 25, 76)( 26, 75)( 27, 77)( 28, 78)( 29, 80)( 30, 79)( 31, 73)
( 32, 74)( 33, 37)( 34, 38)( 35, 36)( 39, 40)( 41, 63)( 42, 64)( 43, 58)
( 44, 57)( 45, 59)( 46, 60)( 47, 62)( 48, 61)( 49, 54)( 50, 53)( 97,166)
( 98,165)( 99,163)(100,164)(101,162)(102,161)(103,167)(104,168)(105,192)
(106,191)(107,185)(108,186)(109,188)(110,187)(111,189)(112,190)(113,181)
(114,182)(115,180)(116,179)(117,177)(118,178)(119,184)(120,183)(121,171)
(122,172)(123,174)(124,173)(125,175)(126,176)(127,170)(128,169)(129,134)
(130,133)(137,160)(138,159)(139,153)(140,154)(141,156)(142,155)(143,157)
(144,158)(145,149)(146,150)(147,148)(151,152);
s3 := Sym(194)!(193,194);
poly := sub<Sym(194)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 >;

to this polytope