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Polytope of Type {38,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,6,4}*1824a
Also Known As : {{38,6|2},{6,4|2}}. if this polytope has another name.
Group : SmallGroup(1824,1141)
Rank : 4
Schlafli Type : {38,6,4}
Number of vertices, edges, etc : 38, 114, 12, 4
Order of s0s1s2s3 : 228
Order of s0s1s2s3s2s1 : 2
Special Properties :
   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 : {38,2,4}*608
   6-fold quotients : {19,2,4}*304, {38,2,2}*304
   12-fold quotients : {19,2,2}*152
   19-fold quotients : {2,6,4}*96a
   38-fold quotients : {2,6,2}*48
   57-fold quotients : {2,2,4}*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)
(115,116)(117,133)(118,132)(119,131)(120,130)(121,129)(122,128)(123,127)
(124,126)(134,154)(135,153)(136,171)(137,170)(138,169)(139,168)(140,167)
(141,166)(142,165)(143,164)(144,163)(145,162)(146,161)(147,160)(148,159)
(149,158)(150,157)(151,156)(152,155)(172,173)(174,190)(175,189)(176,188)
(177,187)(178,186)(179,185)(180,184)(181,183)(191,211)(192,210)(193,228)
(194,227)(195,226)(196,225)(197,224)(198,223)(199,222)(200,221)(201,220)
(202,219)(203,218)(204,217)(205,216)(206,215)(207,214)(208,213)(209,212);;
s2 := (  1, 20)(  2, 21)(  3, 22)(  4, 23)(  5, 24)(  6, 25)(  7, 26)(  8, 27)
(  9, 28)( 10, 29)( 11, 30)( 12, 31)( 13, 32)( 14, 33)( 15, 34)( 16, 35)
( 17, 36)( 18, 37)( 19, 38)( 58, 77)( 59, 78)( 60, 79)( 61, 80)( 62, 81)
( 63, 82)( 64, 83)( 65, 84)( 66, 85)( 67, 86)( 68, 87)( 69, 88)( 70, 89)
( 71, 90)( 72, 91)( 73, 92)( 74, 93)( 75, 94)( 76, 95)(115,191)(116,192)
(117,193)(118,194)(119,195)(120,196)(121,197)(122,198)(123,199)(124,200)
(125,201)(126,202)(127,203)(128,204)(129,205)(130,206)(131,207)(132,208)
(133,209)(134,172)(135,173)(136,174)(137,175)(138,176)(139,177)(140,178)
(141,179)(142,180)(143,181)(144,182)(145,183)(146,184)(147,185)(148,186)
(149,187)(150,188)(151,189)(152,190)(153,210)(154,211)(155,212)(156,213)
(157,214)(158,215)(159,216)(160,217)(161,218)(162,219)(163,220)(164,221)
(165,222)(166,223)(167,224)(168,225)(169,226)(170,227)(171,228);;
s3 := (  1,115)(  2,116)(  3,117)(  4,118)(  5,119)(  6,120)(  7,121)(  8,122)
(  9,123)( 10,124)( 11,125)( 12,126)( 13,127)( 14,128)( 15,129)( 16,130)
( 17,131)( 18,132)( 19,133)( 20,134)( 21,135)( 22,136)( 23,137)( 24,138)
( 25,139)( 26,140)( 27,141)( 28,142)( 29,143)( 30,144)( 31,145)( 32,146)
( 33,147)( 34,148)( 35,149)( 36,150)( 37,151)( 38,152)( 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)( 58,172)( 59,173)( 60,174)( 61,175)( 62,176)( 63,177)( 64,178)
( 65,179)( 66,180)( 67,181)( 68,182)( 69,183)( 70,184)( 71,185)( 72,186)
( 73,187)( 74,188)( 75,189)( 76,190)( 77,191)( 78,192)( 79,193)( 80,194)
( 81,195)( 82,196)( 83,197)( 84,198)( 85,199)( 86,200)( 87,201)( 88,202)
( 89,203)( 90,204)( 91,205)( 92,206)( 93,207)( 94,208)( 95,209)( 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);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
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(228)!(  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(228)!(  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)(115,116)(117,133)(118,132)(119,131)(120,130)(121,129)(122,128)
(123,127)(124,126)(134,154)(135,153)(136,171)(137,170)(138,169)(139,168)
(140,167)(141,166)(142,165)(143,164)(144,163)(145,162)(146,161)(147,160)
(148,159)(149,158)(150,157)(151,156)(152,155)(172,173)(174,190)(175,189)
(176,188)(177,187)(178,186)(179,185)(180,184)(181,183)(191,211)(192,210)
(193,228)(194,227)(195,226)(196,225)(197,224)(198,223)(199,222)(200,221)
(201,220)(202,219)(203,218)(204,217)(205,216)(206,215)(207,214)(208,213)
(209,212);
s2 := Sym(228)!(  1, 20)(  2, 21)(  3, 22)(  4, 23)(  5, 24)(  6, 25)(  7, 26)
(  8, 27)(  9, 28)( 10, 29)( 11, 30)( 12, 31)( 13, 32)( 14, 33)( 15, 34)
( 16, 35)( 17, 36)( 18, 37)( 19, 38)( 58, 77)( 59, 78)( 60, 79)( 61, 80)
( 62, 81)( 63, 82)( 64, 83)( 65, 84)( 66, 85)( 67, 86)( 68, 87)( 69, 88)
( 70, 89)( 71, 90)( 72, 91)( 73, 92)( 74, 93)( 75, 94)( 76, 95)(115,191)
(116,192)(117,193)(118,194)(119,195)(120,196)(121,197)(122,198)(123,199)
(124,200)(125,201)(126,202)(127,203)(128,204)(129,205)(130,206)(131,207)
(132,208)(133,209)(134,172)(135,173)(136,174)(137,175)(138,176)(139,177)
(140,178)(141,179)(142,180)(143,181)(144,182)(145,183)(146,184)(147,185)
(148,186)(149,187)(150,188)(151,189)(152,190)(153,210)(154,211)(155,212)
(156,213)(157,214)(158,215)(159,216)(160,217)(161,218)(162,219)(163,220)
(164,221)(165,222)(166,223)(167,224)(168,225)(169,226)(170,227)(171,228);
s3 := Sym(228)!(  1,115)(  2,116)(  3,117)(  4,118)(  5,119)(  6,120)(  7,121)
(  8,122)(  9,123)( 10,124)( 11,125)( 12,126)( 13,127)( 14,128)( 15,129)
( 16,130)( 17,131)( 18,132)( 19,133)( 20,134)( 21,135)( 22,136)( 23,137)
( 24,138)( 25,139)( 26,140)( 27,141)( 28,142)( 29,143)( 30,144)( 31,145)
( 32,146)( 33,147)( 34,148)( 35,149)( 36,150)( 37,151)( 38,152)( 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)( 58,172)( 59,173)( 60,174)( 61,175)( 62,176)( 63,177)
( 64,178)( 65,179)( 66,180)( 67,181)( 68,182)( 69,183)( 70,184)( 71,185)
( 72,186)( 73,187)( 74,188)( 75,189)( 76,190)( 77,191)( 78,192)( 79,193)
( 80,194)( 81,195)( 82,196)( 83,197)( 84,198)( 85,199)( 86,200)( 87,201)
( 88,202)( 89,203)( 90,204)( 91,205)( 92,206)( 93,207)( 94,208)( 95,209)
( 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);
poly := sub<Sym(228)|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, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, 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 >; 
 
References : None.
to this polytope