Polytope of Type {12,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4}*384c
if this polytope has a name.
Group : SmallGroup(384,5567)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 48, 96, 16
Order of s0s1s2 : 12
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {12,4,2} of size 768
Vertex Figure Of :
   {2,12,4} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4}*192a
   4-fold quotients : {12,4}*96c
   8-fold quotients : {6,4}*48c
   16-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,8}*768g, {12,8}*768h, {24,4}*768g, {24,4}*768h, {12,4}*768b
   3-fold covers : {36,4}*1152c
   5-fold covers : {60,4}*1920c
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0> of order 2.
      8 facets:
         8 of {12}*24
      28 vertex figures:
         20 of {4}*8
         8 of {2}*4
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 2.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 2.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s2, s1*s0*s1*s2*s1*s0*s2*s1> of order 4.
      4 facets:
         4 of {12}*24
      18 vertex figures:
         6 of {4}*8
         12 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0> of order 4.
      4 facets:
         4 of {12}*24
      16 vertex figures:
         8 of {4}*8
         8 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2> of order 4.
      4 facets:
         4 of {12}*24
      12 vertex figures:
         12 of {4}*8

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