Polytope of Type {38,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,12,2}*1824
if this polytope has a name.
Group : SmallGroup(1824,1131)
Rank : 4
Schlafli Type : {38,12,2}
Number of vertices, edges, etc : 38, 228, 12, 2
Order of s₀s₁s₂s₃ : 228
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {38,6,2}*912
   3-fold quotients : {38,4,2}*608
   6-fold quotients : {38,2,2}*304
   12-fold quotients : {19,2,2}*152
   19-fold quotients : {2,12,2}*96
   38-fold quotients : {2,6,2}*48
   57-fold quotients : {2,4,2}*32
   76-fold quotients : {2,3,2}*24
   114-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)
( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)( 45, 52)
( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)
( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 78, 95)( 79, 94)( 80, 93)( 81, 92)
( 82, 91)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 97,114)( 98,113)( 99,112)
(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(116,133)(117,132)
(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(135,152)
(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)(143,144)
(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)
(162,163)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)(179,184)
(180,183)(181,182)(192,209)(193,208)(194,207)(195,206)(196,205)(197,204)
(198,203)(199,202)(200,201)(211,228)(212,227)(213,226)(214,225)(215,224)
(216,223)(217,222)(218,221)(219,220);;
s1 := (  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)(  9, 13)
( 10, 12)( 20, 40)( 21, 39)( 22, 57)( 23, 56)( 24, 55)( 25, 54)( 26, 53)
( 27, 52)( 28, 51)( 29, 50)( 30, 49)( 31, 48)( 32, 47)( 33, 46)( 34, 45)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 58, 59)( 60, 76)( 61, 75)( 62, 74)
( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 77, 97)( 78, 96)( 79,114)
( 80,113)( 81,112)( 82,111)( 83,110)( 84,109)( 85,108)( 86,107)( 87,106)
( 88,105)( 89,104)( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)( 95, 98)
(115,173)(116,172)(117,190)(118,189)(119,188)(120,187)(121,186)(122,185)
(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,178)(130,177)
(131,176)(132,175)(133,174)(134,211)(135,210)(136,228)(137,227)(138,226)
(139,225)(140,224)(141,223)(142,222)(143,221)(144,220)(145,219)(146,218)
(147,217)(148,216)(149,215)(150,214)(151,213)(152,212)(153,192)(154,191)
(155,209)(156,208)(157,207)(158,206)(159,205)(160,204)(161,203)(162,202)
(163,201)(164,200)(165,199)(166,198)(167,197)(168,196)(169,195)(170,194)
(171,193);;
s2 := (  1,134)(  2,135)(  3,136)(  4,137)(  5,138)(  6,139)(  7,140)(  8,141)
(  9,142)( 10,143)( 11,144)( 12,145)( 13,146)( 14,147)( 15,148)( 16,149)
( 17,150)( 18,151)( 19,152)( 20,115)( 21,116)( 22,117)( 23,118)( 24,119)
( 25,120)( 26,121)( 27,122)( 28,123)( 29,124)( 30,125)( 31,126)( 32,127)
( 33,128)( 34,129)( 35,130)( 36,131)( 37,132)( 38,133)( 39,153)( 40,154)
( 41,155)( 42,156)( 43,157)( 44,158)( 45,159)( 46,160)( 47,161)( 48,162)
( 49,163)( 50,164)( 51,165)( 52,166)( 53,167)( 54,168)( 55,169)( 56,170)
( 57,171)( 58,191)( 59,192)( 60,193)( 61,194)( 62,195)( 63,196)( 64,197)
( 65,198)( 66,199)( 67,200)( 68,201)( 69,202)( 70,203)( 71,204)( 72,205)
( 73,206)( 74,207)( 75,208)( 76,209)( 77,172)( 78,173)( 79,174)( 80,175)
( 81,176)( 82,177)( 83,178)( 84,179)( 85,180)( 86,181)( 87,182)( 88,183)
( 89,184)( 90,185)( 91,186)( 92,187)( 93,188)( 94,189)( 95,190)( 96,210)
( 97,211)( 98,212)( 99,213)(100,214)(101,215)(102,216)(103,217)(104,218)
(105,219)(106,220)(107,221)(108,222)(109,223)(110,224)(111,225)(112,226)
(113,227)(114,228);;
s3 := (229,230);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*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, 
s0*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*s0*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*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(230)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)
(  9, 12)( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)
( 27, 32)( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)
( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 78, 95)( 79, 94)( 80, 93)
( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 97,114)( 98,113)
( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(116,133)
(117,132)(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)
(135,152)(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)
(143,144)(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)
(161,164)(162,163)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)
(179,184)(180,183)(181,182)(192,209)(193,208)(194,207)(195,206)(196,205)
(197,204)(198,203)(199,202)(200,201)(211,228)(212,227)(213,226)(214,225)
(215,224)(216,223)(217,222)(218,221)(219,220);
s1 := Sym(230)!(  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)
(  9, 13)( 10, 12)( 20, 40)( 21, 39)( 22, 57)( 23, 56)( 24, 55)( 25, 54)
( 26, 53)( 27, 52)( 28, 51)( 29, 50)( 30, 49)( 31, 48)( 32, 47)( 33, 46)
( 34, 45)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 58, 59)( 60, 76)( 61, 75)
( 62, 74)( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 77, 97)( 78, 96)
( 79,114)( 80,113)( 81,112)( 82,111)( 83,110)( 84,109)( 85,108)( 86,107)
( 87,106)( 88,105)( 89,104)( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)
( 95, 98)(115,173)(116,172)(117,190)(118,189)(119,188)(120,187)(121,186)
(122,185)(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,178)
(130,177)(131,176)(132,175)(133,174)(134,211)(135,210)(136,228)(137,227)
(138,226)(139,225)(140,224)(141,223)(142,222)(143,221)(144,220)(145,219)
(146,218)(147,217)(148,216)(149,215)(150,214)(151,213)(152,212)(153,192)
(154,191)(155,209)(156,208)(157,207)(158,206)(159,205)(160,204)(161,203)
(162,202)(163,201)(164,200)(165,199)(166,198)(167,197)(168,196)(169,195)
(170,194)(171,193);
s2 := Sym(230)!(  1,134)(  2,135)(  3,136)(  4,137)(  5,138)(  6,139)(  7,140)
(  8,141)(  9,142)( 10,143)( 11,144)( 12,145)( 13,146)( 14,147)( 15,148)
( 16,149)( 17,150)( 18,151)( 19,152)( 20,115)( 21,116)( 22,117)( 23,118)
( 24,119)( 25,120)( 26,121)( 27,122)( 28,123)( 29,124)( 30,125)( 31,126)
( 32,127)( 33,128)( 34,129)( 35,130)( 36,131)( 37,132)( 38,133)( 39,153)
( 40,154)( 41,155)( 42,156)( 43,157)( 44,158)( 45,159)( 46,160)( 47,161)
( 48,162)( 49,163)( 50,164)( 51,165)( 52,166)( 53,167)( 54,168)( 55,169)
( 56,170)( 57,171)( 58,191)( 59,192)( 60,193)( 61,194)( 62,195)( 63,196)
( 64,197)( 65,198)( 66,199)( 67,200)( 68,201)( 69,202)( 70,203)( 71,204)
( 72,205)( 73,206)( 74,207)( 75,208)( 76,209)( 77,172)( 78,173)( 79,174)
( 80,175)( 81,176)( 82,177)( 83,178)( 84,179)( 85,180)( 86,181)( 87,182)
( 88,183)( 89,184)( 90,185)( 91,186)( 92,187)( 93,188)( 94,189)( 95,190)
( 96,210)( 97,211)( 98,212)( 99,213)(100,214)(101,215)(102,216)(103,217)
(104,218)(105,219)(106,220)(107,221)(108,222)(109,223)(110,224)(111,225)
(112,226)(113,227)(114,228);
s3 := Sym(230)!(229,230);
poly := sub<Sym(230)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*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, 
s0*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*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope