Polytope of Type {4,12}

Play with this polytope as a twisty puzzle

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

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