Polytope of Type {12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4}*384b
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}*96b
   8-fold quotients : {6,4}*48c
   16-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,4}*768e, {24,4}*768f, {12,8}*768e, {12,8}*768f, {12,4}*768b
   3-fold covers : {36,4}*1152b
   5-fold covers : {60,4}*1920b
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, 13)(  2, 14)(  3, 15)(  4, 16)(  5,  9)(  6, 10)(  7, 11)(  8, 12)
( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 25)( 22, 26)( 23, 27)( 24, 28)
( 33, 45)( 34, 46)( 35, 47)( 36, 48)( 37, 41)( 38, 42)( 39, 43)( 40, 44)
( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 57)( 54, 58)( 55, 59)( 56, 60)
( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)
( 81, 93)( 82, 94)( 83, 95)( 84, 96)( 85, 89)( 86, 90)( 87, 91)( 88, 92)
( 97,109)( 98,110)( 99,111)(100,112)(101,105)(102,106)(103,107)(104,108)
(113,125)(114,126)(115,127)(116,128)(117,121)(118,122)(119,123)(120,124)
(129,141)(130,142)(131,143)(132,144)(133,137)(134,138)(135,139)(136,140)
(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)(152,156)
(161,173)(162,174)(163,175)(164,176)(165,169)(166,170)(167,171)(168,172)
(177,189)(178,190)(179,191)(180,192)(181,185)(182,186)(183,187)(184,188);;
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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, 13)(  2, 14)(  3, 15)(  4, 16)(  5,  9)(  6, 10)(  7, 11)
(  8, 12)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 25)( 22, 26)( 23, 27)
( 24, 28)( 33, 45)( 34, 46)( 35, 47)( 36, 48)( 37, 41)( 38, 42)( 39, 43)
( 40, 44)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 57)( 54, 58)( 55, 59)
( 56, 60)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)
( 72, 76)( 81, 93)( 82, 94)( 83, 95)( 84, 96)( 85, 89)( 86, 90)( 87, 91)
( 88, 92)( 97,109)( 98,110)( 99,111)(100,112)(101,105)(102,106)(103,107)
(104,108)(113,125)(114,126)(115,127)(116,128)(117,121)(118,122)(119,123)
(120,124)(129,141)(130,142)(131,143)(132,144)(133,137)(134,138)(135,139)
(136,140)(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)
(152,156)(161,173)(162,174)(163,175)(164,176)(165,169)(166,170)(167,171)
(168,172)(177,189)(178,190)(179,191)(180,192)(181,185)(182,186)(183,187)
(184,188);
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope