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Polytope of Type {2,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,8}*768a
if this polytope has a name.
Group : SmallGroup(768,1086301)
Rank : 4
Schlafli Type : {2,6,8}
Number of vertices, edges, etc : 2, 24, 96, 32
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 : {2,3,8}*384
   8-fold quotients : {2,3,4}*96
   16-fold quotients : {2,3,4}*48
   32-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  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);;
s2 := (  3, 43)(  4, 44)(  5, 48)(  6, 47)(  7, 46)(  8, 45)(  9, 49)( 10, 50)
( 11, 35)( 12, 36)( 13, 40)( 14, 39)( 15, 38)( 16, 37)( 17, 41)( 18, 42)
( 19, 52)( 20, 51)( 21, 55)( 22, 56)( 23, 53)( 24, 54)( 25, 58)( 26, 57)
( 27, 66)( 28, 65)( 29, 61)( 30, 62)( 31, 63)( 32, 64)( 33, 60)( 34, 59)
( 67, 75)( 68, 76)( 69, 80)( 70, 79)( 71, 78)( 72, 77)( 73, 81)( 74, 82)
( 83, 84)( 85, 87)( 86, 88)( 89, 90)( 91, 98)( 92, 97)( 99,140)(100,139)
(101,143)(102,144)(103,141)(104,142)(105,146)(106,145)(107,132)(108,131)
(109,135)(110,136)(111,133)(112,134)(113,138)(114,137)(115,147)(116,148)
(117,152)(118,151)(119,150)(120,149)(121,153)(122,154)(123,161)(124,162)
(125,158)(126,157)(127,160)(128,159)(129,155)(130,156)(163,172)(164,171)
(165,175)(166,176)(167,173)(168,174)(169,178)(170,177)(181,184)(182,183)
(187,193)(188,194)(189,190)(191,192);;
s3 := (  3,127)(  4,128)(  5,129)(  6,130)(  7,123)(  8,124)(  9,125)( 10,126)
( 11,119)( 12,120)( 13,121)( 14,122)( 15,115)( 16,116)( 17,117)( 18,118)
( 19,112)( 20,111)( 21,114)( 22,113)( 23,108)( 24,107)( 25,110)( 26,109)
( 27,104)( 28,103)( 29,106)( 30,105)( 31,100)( 32, 99)( 33,102)( 34,101)
( 35,159)( 36,160)( 37,161)( 38,162)( 39,155)( 40,156)( 41,157)( 42,158)
( 43,151)( 44,152)( 45,153)( 46,154)( 47,147)( 48,148)( 49,149)( 50,150)
( 51,144)( 52,143)( 53,146)( 54,145)( 55,140)( 56,139)( 57,142)( 58,141)
( 59,136)( 60,135)( 61,138)( 62,137)( 63,132)( 64,131)( 65,134)( 66,133)
( 67,191)( 68,192)( 69,193)( 70,194)( 71,187)( 72,188)( 73,189)( 74,190)
( 75,183)( 76,184)( 77,185)( 78,186)( 79,179)( 80,180)( 81,181)( 82,182)
( 83,176)( 84,175)( 85,178)( 86,177)( 87,172)( 88,171)( 89,174)( 90,173)
( 91,168)( 92,167)( 93,170)( 94,169)( 95,164)( 96,163)( 97,166)( 98,165);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s2*s1*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := 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);
s2 := Sym(194)!(  3, 43)(  4, 44)(  5, 48)(  6, 47)(  7, 46)(  8, 45)(  9, 49)
( 10, 50)( 11, 35)( 12, 36)( 13, 40)( 14, 39)( 15, 38)( 16, 37)( 17, 41)
( 18, 42)( 19, 52)( 20, 51)( 21, 55)( 22, 56)( 23, 53)( 24, 54)( 25, 58)
( 26, 57)( 27, 66)( 28, 65)( 29, 61)( 30, 62)( 31, 63)( 32, 64)( 33, 60)
( 34, 59)( 67, 75)( 68, 76)( 69, 80)( 70, 79)( 71, 78)( 72, 77)( 73, 81)
( 74, 82)( 83, 84)( 85, 87)( 86, 88)( 89, 90)( 91, 98)( 92, 97)( 99,140)
(100,139)(101,143)(102,144)(103,141)(104,142)(105,146)(106,145)(107,132)
(108,131)(109,135)(110,136)(111,133)(112,134)(113,138)(114,137)(115,147)
(116,148)(117,152)(118,151)(119,150)(120,149)(121,153)(122,154)(123,161)
(124,162)(125,158)(126,157)(127,160)(128,159)(129,155)(130,156)(163,172)
(164,171)(165,175)(166,176)(167,173)(168,174)(169,178)(170,177)(181,184)
(182,183)(187,193)(188,194)(189,190)(191,192);
s3 := Sym(194)!(  3,127)(  4,128)(  5,129)(  6,130)(  7,123)(  8,124)(  9,125)
( 10,126)( 11,119)( 12,120)( 13,121)( 14,122)( 15,115)( 16,116)( 17,117)
( 18,118)( 19,112)( 20,111)( 21,114)( 22,113)( 23,108)( 24,107)( 25,110)
( 26,109)( 27,104)( 28,103)( 29,106)( 30,105)( 31,100)( 32, 99)( 33,102)
( 34,101)( 35,159)( 36,160)( 37,161)( 38,162)( 39,155)( 40,156)( 41,157)
( 42,158)( 43,151)( 44,152)( 45,153)( 46,154)( 47,147)( 48,148)( 49,149)
( 50,150)( 51,144)( 52,143)( 53,146)( 54,145)( 55,140)( 56,139)( 57,142)
( 58,141)( 59,136)( 60,135)( 61,138)( 62,137)( 63,132)( 64,131)( 65,134)
( 66,133)( 67,191)( 68,192)( 69,193)( 70,194)( 71,187)( 72,188)( 73,189)
( 74,190)( 75,183)( 76,184)( 77,185)( 78,186)( 79,179)( 80,180)( 81,181)
( 82,182)( 83,176)( 84,175)( 85,178)( 86,177)( 87,172)( 88,171)( 89,174)
( 90,173)( 91,168)( 92,167)( 93,170)( 94,169)( 95,164)( 96,163)( 97,166)
( 98,165);
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s2*s1*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1 >; 
 

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