Polytope of Type {6,8,2}

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

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

Permutation Representation (Magma) :

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

to this polytope