Polytope of Type {24,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8}*768m
if this polytope has a name.
Group : SmallGroup(768,1086649)
Rank : 3
Schlafli Type : {24,8}
Number of vertices, edges, etc : 48, 192, 16
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 : {12,8}*384g, {24,4}*384f
   4-fold quotients : {12,4}*192c, {6,8}*192c
   8-fold quotients : {6,4}*96
   16-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,4}*24, {6,2}*24
   64-fold quotients : {3,2}*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=<s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 2.
      8 facets:
         8 of {24}*48
      24 vertex figures:
         24 of {8}*16
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 2.
      8 facets:
         8 of {24}*48
      24 vertex figures:
         24 of {8}*16

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