Polytope of Type {4,12}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope