Polytope of Type {12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4}*384e
if this polytope has a name.
Group : SmallGroup(384,18044)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 48, 96, 16
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
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}*192b
   4-fold quotients : {6,4}*96
   8-fold quotients : {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   16-fold quotients : {3,4}*24, {6,2}*24
   24-fold quotients : {2,4}*16
   32-fold quotients : {3,2}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,8}*768o, {12,8}*768p, {12,4}*768e
   3-fold covers : {36,4}*1152e, {12,12}*1152h, {12,12}*1152s
   5-fold covers : {12,20}*1920b, {60,4}*1920e
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope