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Polytope of Type {12,38}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,38}*912
Also Known As : {12,38|2}. if this polytope has another name.
Group : SmallGroup(912,147)
Rank : 3
Schlafli Type : {12,38}
Number of vertices, edges, etc : 12, 228, 38
Order of s0s1s2 : 228
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,38,2} of size 1824
Vertex Figure Of :
   {2,12,38} of size 1824
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,38}*456
   3-fold quotients : {4,38}*304
   6-fold quotients : {2,38}*152
   12-fold quotients : {2,19}*76
   19-fold quotients : {12,2}*48
   38-fold quotients : {6,2}*24
   57-fold quotients : {4,2}*16
   76-fold quotients : {3,2}*12
   114-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,38}*1824, {12,76}*1824
Permutation Representation (GAP) :
s0 := ( 20, 39)( 21, 40)( 22, 41)( 23, 42)( 24, 43)( 25, 44)( 26, 45)( 27, 46)
( 28, 47)( 29, 48)( 30, 49)( 31, 50)( 32, 51)( 33, 52)( 34, 53)( 35, 54)
( 36, 55)( 37, 56)( 38, 57)( 77, 96)( 78, 97)( 79, 98)( 80, 99)( 81,100)
( 82,101)( 83,102)( 84,103)( 85,104)( 86,105)( 87,106)( 88,107)( 89,108)
( 90,109)( 91,110)( 92,111)( 93,112)( 94,113)( 95,114)(115,172)(116,173)
(117,174)(118,175)(119,176)(120,177)(121,178)(122,179)(123,180)(124,181)
(125,182)(126,183)(127,184)(128,185)(129,186)(130,187)(131,188)(132,189)
(133,190)(134,210)(135,211)(136,212)(137,213)(138,214)(139,215)(140,216)
(141,217)(142,218)(143,219)(144,220)(145,221)(146,222)(147,223)(148,224)
(149,225)(150,226)(151,227)(152,228)(153,191)(154,192)(155,193)(156,194)
(157,195)(158,196)(159,197)(160,198)(161,199)(162,200)(163,201)(164,202)
(165,203)(166,204)(167,205)(168,206)(169,207)(170,208)(171,209);;
s1 := (  1,134)(  2,152)(  3,151)(  4,150)(  5,149)(  6,148)(  7,147)(  8,146)
(  9,145)( 10,144)( 11,143)( 12,142)( 13,141)( 14,140)( 15,139)( 16,138)
( 17,137)( 18,136)( 19,135)( 20,115)( 21,133)( 22,132)( 23,131)( 24,130)
( 25,129)( 26,128)( 27,127)( 28,126)( 29,125)( 30,124)( 31,123)( 32,122)
( 33,121)( 34,120)( 35,119)( 36,118)( 37,117)( 38,116)( 39,153)( 40,171)
( 41,170)( 42,169)( 43,168)( 44,167)( 45,166)( 46,165)( 47,164)( 48,163)
( 49,162)( 50,161)( 51,160)( 52,159)( 53,158)( 54,157)( 55,156)( 56,155)
( 57,154)( 58,191)( 59,209)( 60,208)( 61,207)( 62,206)( 63,205)( 64,204)
( 65,203)( 66,202)( 67,201)( 68,200)( 69,199)( 70,198)( 71,197)( 72,196)
( 73,195)( 74,194)( 75,193)( 76,192)( 77,172)( 78,190)( 79,189)( 80,188)
( 81,187)( 82,186)( 83,185)( 84,184)( 85,183)( 86,182)( 87,181)( 88,180)
( 89,179)( 90,178)( 91,177)( 92,176)( 93,175)( 94,174)( 95,173)( 96,210)
( 97,228)( 98,227)( 99,226)(100,225)(101,224)(102,223)(103,222)(104,221)
(105,220)(106,219)(107,218)(108,217)(109,216)(110,215)(111,214)(112,213)
(113,212)(114,211);;
s2 := (  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)(  9, 13)
( 10, 12)( 20, 21)( 22, 38)( 23, 37)( 24, 36)( 25, 35)( 26, 34)( 27, 33)
( 28, 32)( 29, 31)( 39, 40)( 41, 57)( 42, 56)( 43, 55)( 44, 54)( 45, 53)
( 46, 52)( 47, 51)( 48, 50)( 58, 59)( 60, 76)( 61, 75)( 62, 74)( 63, 73)
( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 77, 78)( 79, 95)( 80, 94)( 81, 93)
( 82, 92)( 83, 91)( 84, 90)( 85, 89)( 86, 88)( 96, 97)( 98,114)( 99,113)
(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(115,116)(117,133)
(118,132)(119,131)(120,130)(121,129)(122,128)(123,127)(124,126)(134,135)
(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)(142,146)(143,145)
(153,154)(155,171)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)
(162,164)(172,173)(174,190)(175,189)(176,188)(177,187)(178,186)(179,185)
(180,184)(181,183)(191,192)(193,209)(194,208)(195,207)(196,206)(197,205)
(198,204)(199,203)(200,202)(210,211)(212,228)(213,227)(214,226)(215,225)
(216,224)(217,223)(218,222)(219,221);;
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*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(228)!( 20, 39)( 21, 40)( 22, 41)( 23, 42)( 24, 43)( 25, 44)( 26, 45)
( 27, 46)( 28, 47)( 29, 48)( 30, 49)( 31, 50)( 32, 51)( 33, 52)( 34, 53)
( 35, 54)( 36, 55)( 37, 56)( 38, 57)( 77, 96)( 78, 97)( 79, 98)( 80, 99)
( 81,100)( 82,101)( 83,102)( 84,103)( 85,104)( 86,105)( 87,106)( 88,107)
( 89,108)( 90,109)( 91,110)( 92,111)( 93,112)( 94,113)( 95,114)(115,172)
(116,173)(117,174)(118,175)(119,176)(120,177)(121,178)(122,179)(123,180)
(124,181)(125,182)(126,183)(127,184)(128,185)(129,186)(130,187)(131,188)
(132,189)(133,190)(134,210)(135,211)(136,212)(137,213)(138,214)(139,215)
(140,216)(141,217)(142,218)(143,219)(144,220)(145,221)(146,222)(147,223)
(148,224)(149,225)(150,226)(151,227)(152,228)(153,191)(154,192)(155,193)
(156,194)(157,195)(158,196)(159,197)(160,198)(161,199)(162,200)(163,201)
(164,202)(165,203)(166,204)(167,205)(168,206)(169,207)(170,208)(171,209);
s1 := Sym(228)!(  1,134)(  2,152)(  3,151)(  4,150)(  5,149)(  6,148)(  7,147)
(  8,146)(  9,145)( 10,144)( 11,143)( 12,142)( 13,141)( 14,140)( 15,139)
( 16,138)( 17,137)( 18,136)( 19,135)( 20,115)( 21,133)( 22,132)( 23,131)
( 24,130)( 25,129)( 26,128)( 27,127)( 28,126)( 29,125)( 30,124)( 31,123)
( 32,122)( 33,121)( 34,120)( 35,119)( 36,118)( 37,117)( 38,116)( 39,153)
( 40,171)( 41,170)( 42,169)( 43,168)( 44,167)( 45,166)( 46,165)( 47,164)
( 48,163)( 49,162)( 50,161)( 51,160)( 52,159)( 53,158)( 54,157)( 55,156)
( 56,155)( 57,154)( 58,191)( 59,209)( 60,208)( 61,207)( 62,206)( 63,205)
( 64,204)( 65,203)( 66,202)( 67,201)( 68,200)( 69,199)( 70,198)( 71,197)
( 72,196)( 73,195)( 74,194)( 75,193)( 76,192)( 77,172)( 78,190)( 79,189)
( 80,188)( 81,187)( 82,186)( 83,185)( 84,184)( 85,183)( 86,182)( 87,181)
( 88,180)( 89,179)( 90,178)( 91,177)( 92,176)( 93,175)( 94,174)( 95,173)
( 96,210)( 97,228)( 98,227)( 99,226)(100,225)(101,224)(102,223)(103,222)
(104,221)(105,220)(106,219)(107,218)(108,217)(109,216)(110,215)(111,214)
(112,213)(113,212)(114,211);
s2 := Sym(228)!(  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)
(  9, 13)( 10, 12)( 20, 21)( 22, 38)( 23, 37)( 24, 36)( 25, 35)( 26, 34)
( 27, 33)( 28, 32)( 29, 31)( 39, 40)( 41, 57)( 42, 56)( 43, 55)( 44, 54)
( 45, 53)( 46, 52)( 47, 51)( 48, 50)( 58, 59)( 60, 76)( 61, 75)( 62, 74)
( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 77, 78)( 79, 95)( 80, 94)
( 81, 93)( 82, 92)( 83, 91)( 84, 90)( 85, 89)( 86, 88)( 96, 97)( 98,114)
( 99,113)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(115,116)
(117,133)(118,132)(119,131)(120,130)(121,129)(122,128)(123,127)(124,126)
(134,135)(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)(142,146)
(143,145)(153,154)(155,171)(156,170)(157,169)(158,168)(159,167)(160,166)
(161,165)(162,164)(172,173)(174,190)(175,189)(176,188)(177,187)(178,186)
(179,185)(180,184)(181,183)(191,192)(193,209)(194,208)(195,207)(196,206)
(197,205)(198,204)(199,203)(200,202)(210,211)(212,228)(213,227)(214,226)
(215,225)(216,224)(217,223)(218,222)(219,221);
poly := sub<Sym(228)|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*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
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