Polytope of Type {8,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,24}*768m
if this polytope has a name.
Group : SmallGroup(768,1086649)
Rank : 3
Schlafli Type : {8,24}
Number of vertices, edges, etc : 16, 192, 48
Order of s0s1s2 : 6
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,12}*384g, {4,24}*384f
   4-fold quotients : {4,12}*192c, {8,6}*192c
   8-fold quotients : {4,6}*96
   16-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {4,3}*24, {2,6}*24
   64-fold quotients : {2,3}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1> of order 2.
      24 facets:
         24 of {8}*16
      8 vertex figures:
         8 of {24}*48
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 2.
      24 facets:
         24 of {8}*16
      8 vertex figures:
         8 of {24}*48

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