Polytope of Type {12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*384c
if this polytope has a name.
Group : SmallGroup(384,17986)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 16, 96, 16
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {12,12,2} of size 768
Vertex Figure Of :
   {2,12,12} of size 768
   {3,12,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,12}*192a, {12,6}*192b
   4-fold quotients : {12,3}*96, {6,6}*96
   8-fold quotients : {3,6}*48, {6,3}*48
   16-fold quotients : {3,3}*24
   24-fold quotients : {2,4}*16
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,24}*768a, {12,24}*768b, {12,12}*768a
   3-fold covers : {12,12}*1152f, {12,12}*1152q
   5-fold covers : {12,60}*1920b, {60,12}*1920d
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)( 99,102)(100,101)(103,104)(105,113)
(106,114)(107,118)(108,117)(109,116)(110,115)(111,120)(112,119)(123,126)
(124,125)(127,128)(129,137)(130,138)(131,142)(132,141)(133,140)(134,139)
(135,144)(136,143)(145,146)(147,149)(148,150)(153,162)(154,161)(155,165)
(156,166)(157,163)(158,164)(159,167)(160,168)(169,170)(171,173)(172,174)
(177,186)(178,185)(179,189)(180,190)(181,187)(182,188)(183,191)(184,192);;
s1 := (  1, 57)(  2, 58)(  3, 60)(  4, 59)(  5, 63)(  6, 64)(  7, 61)(  8, 62)
(  9, 49)( 10, 50)( 11, 52)( 12, 51)( 13, 55)( 14, 56)( 15, 53)( 16, 54)
( 17, 65)( 18, 66)( 19, 68)( 20, 67)( 21, 71)( 22, 72)( 23, 69)( 24, 70)
( 25, 81)( 26, 82)( 27, 84)( 28, 83)( 29, 87)( 30, 88)( 31, 85)( 32, 86)
( 33, 73)( 34, 74)( 35, 76)( 36, 75)( 37, 79)( 38, 80)( 39, 77)( 40, 78)
( 41, 89)( 42, 90)( 43, 92)( 44, 91)( 45, 95)( 46, 96)( 47, 93)( 48, 94)
( 97,153)( 98,154)( 99,156)(100,155)(101,159)(102,160)(103,157)(104,158)
(105,145)(106,146)(107,148)(108,147)(109,151)(110,152)(111,149)(112,150)
(113,161)(114,162)(115,164)(116,163)(117,167)(118,168)(119,165)(120,166)
(121,177)(122,178)(123,180)(124,179)(125,183)(126,184)(127,181)(128,182)
(129,169)(130,170)(131,172)(132,171)(133,175)(134,176)(135,173)(136,174)
(137,185)(138,186)(139,188)(140,187)(141,191)(142,192)(143,189)(144,190);;
s2 := (  1,151)(  2,152)(  3,147)(  4,148)(  5,150)(  6,149)(  7,145)(  8,146)
(  9,167)( 10,168)( 11,163)( 12,164)( 13,166)( 14,165)( 15,161)( 16,162)
( 17,159)( 18,160)( 19,155)( 20,156)( 21,158)( 22,157)( 23,153)( 24,154)
( 25,175)( 26,176)( 27,171)( 28,172)( 29,174)( 30,173)( 31,169)( 32,170)
( 33,191)( 34,192)( 35,187)( 36,188)( 37,190)( 38,189)( 39,185)( 40,186)
( 41,183)( 42,184)( 43,179)( 44,180)( 45,182)( 46,181)( 47,177)( 48,178)
( 49,127)( 50,128)( 51,123)( 52,124)( 53,126)( 54,125)( 55,121)( 56,122)
( 57,143)( 58,144)( 59,139)( 60,140)( 61,142)( 62,141)( 63,137)( 64,138)
( 65,135)( 66,136)( 67,131)( 68,132)( 69,134)( 70,133)( 71,129)( 72,130)
( 73,103)( 74,104)( 75, 99)( 76,100)( 77,102)( 78,101)( 79, 97)( 80, 98)
( 81,119)( 82,120)( 83,115)( 84,116)( 85,118)( 86,117)( 87,113)( 88,114)
( 89,111)( 90,112)( 91,107)( 92,108)( 93,110)( 94,109)( 95,105)( 96,106);;
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1*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)( 99,102)(100,101)(103,104)
(105,113)(106,114)(107,118)(108,117)(109,116)(110,115)(111,120)(112,119)
(123,126)(124,125)(127,128)(129,137)(130,138)(131,142)(132,141)(133,140)
(134,139)(135,144)(136,143)(145,146)(147,149)(148,150)(153,162)(154,161)
(155,165)(156,166)(157,163)(158,164)(159,167)(160,168)(169,170)(171,173)
(172,174)(177,186)(178,185)(179,189)(180,190)(181,187)(182,188)(183,191)
(184,192);
s1 := Sym(192)!(  1, 57)(  2, 58)(  3, 60)(  4, 59)(  5, 63)(  6, 64)(  7, 61)
(  8, 62)(  9, 49)( 10, 50)( 11, 52)( 12, 51)( 13, 55)( 14, 56)( 15, 53)
( 16, 54)( 17, 65)( 18, 66)( 19, 68)( 20, 67)( 21, 71)( 22, 72)( 23, 69)
( 24, 70)( 25, 81)( 26, 82)( 27, 84)( 28, 83)( 29, 87)( 30, 88)( 31, 85)
( 32, 86)( 33, 73)( 34, 74)( 35, 76)( 36, 75)( 37, 79)( 38, 80)( 39, 77)
( 40, 78)( 41, 89)( 42, 90)( 43, 92)( 44, 91)( 45, 95)( 46, 96)( 47, 93)
( 48, 94)( 97,153)( 98,154)( 99,156)(100,155)(101,159)(102,160)(103,157)
(104,158)(105,145)(106,146)(107,148)(108,147)(109,151)(110,152)(111,149)
(112,150)(113,161)(114,162)(115,164)(116,163)(117,167)(118,168)(119,165)
(120,166)(121,177)(122,178)(123,180)(124,179)(125,183)(126,184)(127,181)
(128,182)(129,169)(130,170)(131,172)(132,171)(133,175)(134,176)(135,173)
(136,174)(137,185)(138,186)(139,188)(140,187)(141,191)(142,192)(143,189)
(144,190);
s2 := Sym(192)!(  1,151)(  2,152)(  3,147)(  4,148)(  5,150)(  6,149)(  7,145)
(  8,146)(  9,167)( 10,168)( 11,163)( 12,164)( 13,166)( 14,165)( 15,161)
( 16,162)( 17,159)( 18,160)( 19,155)( 20,156)( 21,158)( 22,157)( 23,153)
( 24,154)( 25,175)( 26,176)( 27,171)( 28,172)( 29,174)( 30,173)( 31,169)
( 32,170)( 33,191)( 34,192)( 35,187)( 36,188)( 37,190)( 38,189)( 39,185)
( 40,186)( 41,183)( 42,184)( 43,179)( 44,180)( 45,182)( 46,181)( 47,177)
( 48,178)( 49,127)( 50,128)( 51,123)( 52,124)( 53,126)( 54,125)( 55,121)
( 56,122)( 57,143)( 58,144)( 59,139)( 60,140)( 61,142)( 62,141)( 63,137)
( 64,138)( 65,135)( 66,136)( 67,131)( 68,132)( 69,134)( 70,133)( 71,129)
( 72,130)( 73,103)( 74,104)( 75, 99)( 76,100)( 77,102)( 78,101)( 79, 97)
( 80, 98)( 81,119)( 82,120)( 83,115)( 84,116)( 85,118)( 86,117)( 87,113)
( 88,114)( 89,111)( 90,112)( 91,107)( 92,108)( 93,110)( 94,109)( 95,105)
( 96,106);
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope