Polytope of Type {2,3,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,8}*768
if this polytope has a name.
Group : SmallGroup(768,1086301)
Rank : 4
Schlafli Type : {2,3,8}
Number of vertices, edges, etc : 2, 24, 96, 64
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
   4-fold quotients : {2,3,8}*192
   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, 35)(  4, 36)(  5, 40)(  6, 39)(  7, 38)(  8, 37)(  9, 41)( 10, 42)
( 11, 49)( 12, 50)( 13, 46)( 14, 45)( 15, 48)( 16, 47)( 17, 43)( 18, 44)
( 19, 66)( 20, 65)( 21, 61)( 22, 62)( 23, 63)( 24, 64)( 25, 60)( 26, 59)
( 27, 58)( 28, 57)( 29, 53)( 30, 54)( 31, 55)( 32, 56)( 33, 52)( 34, 51)
( 69, 72)( 70, 71)( 75, 81)( 76, 82)( 77, 78)( 79, 80)( 83, 98)( 84, 97)
( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 92)( 90, 91)( 99,132)(100,131)
(101,135)(102,136)(103,133)(104,134)(105,138)(106,137)(107,146)(108,145)
(109,141)(110,142)(111,143)(112,144)(113,140)(114,139)(115,161)(116,162)
(117,158)(118,157)(119,160)(120,159)(121,155)(122,156)(123,153)(124,154)
(125,150)(126,149)(127,152)(128,151)(129,147)(130,148)(163,164)(165,167)
(166,168)(169,170)(171,178)(172,177)(179,193)(180,194)(181,190)(182,189)
(183,192)(184,191)(185,187)(186,188);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 ];;
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, 35)(  4, 36)(  5, 40)(  6, 39)(  7, 38)(  8, 37)(  9, 41)
( 10, 42)( 11, 49)( 12, 50)( 13, 46)( 14, 45)( 15, 48)( 16, 47)( 17, 43)
( 18, 44)( 19, 66)( 20, 65)( 21, 61)( 22, 62)( 23, 63)( 24, 64)( 25, 60)
( 26, 59)( 27, 58)( 28, 57)( 29, 53)( 30, 54)( 31, 55)( 32, 56)( 33, 52)
( 34, 51)( 69, 72)( 70, 71)( 75, 81)( 76, 82)( 77, 78)( 79, 80)( 83, 98)
( 84, 97)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 92)( 90, 91)( 99,132)
(100,131)(101,135)(102,136)(103,133)(104,134)(105,138)(106,137)(107,146)
(108,145)(109,141)(110,142)(111,143)(112,144)(113,140)(114,139)(115,161)
(116,162)(117,158)(118,157)(119,160)(120,159)(121,155)(122,156)(123,153)
(124,154)(125,150)(126,149)(127,152)(128,151)(129,147)(130,148)(163,164)
(165,167)(166,168)(169,170)(171,178)(172,177)(179,193)(180,194)(181,190)
(182,189)(183,192)(184,191)(185,187)(186,188);
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 >;

to this polytope