Polytope of Type {2,8,6}

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

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

Permutation Representation (Magma) :

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

to this polytope