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Polytope of Type {38,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,4,6}*1824
Also Known As : {{38,4|2},{4,6|2}}. if this polytope has another name.
Group : SmallGroup(1824,1141)
Rank : 4
Schlafli Type : {38,4,6}
Number of vertices, edges, etc : 38, 76, 12, 6
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 : {38,2,6}*912
   3-fold quotients : {38,4,2}*608
   4-fold quotients : {19,2,6}*456, {38,2,3}*456
   6-fold quotients : {38,2,2}*304
   8-fold quotients : {19,2,3}*228
   12-fold quotients : {19,2,2}*152
   19-fold quotients : {2,4,6}*96a
   38-fold quotients : {2,2,6}*48
   57-fold quotients : {2,4,2}*32
   76-fold quotients : {2,2,3}*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, 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)(115,173)(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)(134,192)(135,191)(136,209)(137,208)(138,207)(139,206)(140,205)
(141,204)(142,203)(143,202)(144,201)(145,200)(146,199)(147,198)(148,197)
(149,196)(150,195)(151,194)(152,193)(153,211)(154,210)(155,228)(156,227)
(157,226)(158,225)(159,224)(160,223)(161,222)(162,221)(163,220)(164,219)
(165,218)(166,217)(167,216)(168,215)(169,214)(170,213)(171,212);;
s2 := (  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)( 20,153)( 21,154)( 22,155)( 23,156)( 24,157)
( 25,158)( 26,159)( 27,160)( 28,161)( 29,162)( 30,163)( 31,164)( 32,165)
( 33,166)( 34,167)( 35,168)( 36,169)( 37,170)( 38,171)( 39,134)( 40,135)
( 41,136)( 42,137)( 43,138)( 44,139)( 45,140)( 46,141)( 47,142)( 48,143)
( 49,144)( 50,145)( 51,146)( 52,147)( 53,148)( 54,149)( 55,150)( 56,151)
( 57,152)( 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)( 77,210)( 78,211)( 79,212)( 80,213)
( 81,214)( 82,215)( 83,216)( 84,217)( 85,218)( 86,219)( 87,220)( 88,221)
( 89,222)( 90,223)( 91,224)( 92,225)( 93,226)( 94,227)( 95,228)( 96,191)
( 97,192)( 98,193)( 99,194)(100,195)(101,196)(102,197)(103,198)(104,199)
(105,200)(106,201)(107,202)(108,203)(109,204)(110,205)(111,206)(112,207)
(113,208)(114,209);;
s3 := (  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)(115,134)(116,135)
(117,136)(118,137)(119,138)(120,139)(121,140)(122,141)(123,142)(124,143)
(125,144)(126,145)(127,146)(128,147)(129,148)(130,149)(131,150)(132,151)
(133,152)(172,191)(173,192)(174,193)(175,194)(176,195)(177,196)(178,197)
(179,198)(180,199)(181,200)(182,201)(183,202)(184,203)(185,204)(186,205)
(187,206)(188,207)(189,208)(190,209);;
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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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, 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)(115,173)
(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)(134,192)(135,191)(136,209)(137,208)(138,207)(139,206)
(140,205)(141,204)(142,203)(143,202)(144,201)(145,200)(146,199)(147,198)
(148,197)(149,196)(150,195)(151,194)(152,193)(153,211)(154,210)(155,228)
(156,227)(157,226)(158,225)(159,224)(160,223)(161,222)(162,221)(163,220)
(164,219)(165,218)(166,217)(167,216)(168,215)(169,214)(170,213)(171,212);
s2 := 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)( 20,153)( 21,154)( 22,155)( 23,156)
( 24,157)( 25,158)( 26,159)( 27,160)( 28,161)( 29,162)( 30,163)( 31,164)
( 32,165)( 33,166)( 34,167)( 35,168)( 36,169)( 37,170)( 38,171)( 39,134)
( 40,135)( 41,136)( 42,137)( 43,138)( 44,139)( 45,140)( 46,141)( 47,142)
( 48,143)( 49,144)( 50,145)( 51,146)( 52,147)( 53,148)( 54,149)( 55,150)
( 56,151)( 57,152)( 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)( 77,210)( 78,211)( 79,212)
( 80,213)( 81,214)( 82,215)( 83,216)( 84,217)( 85,218)( 86,219)( 87,220)
( 88,221)( 89,222)( 90,223)( 91,224)( 92,225)( 93,226)( 94,227)( 95,228)
( 96,191)( 97,192)( 98,193)( 99,194)(100,195)(101,196)(102,197)(103,198)
(104,199)(105,200)(106,201)(107,202)(108,203)(109,204)(110,205)(111,206)
(112,207)(113,208)(114,209);
s3 := 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)(115,134)
(116,135)(117,136)(118,137)(119,138)(120,139)(121,140)(122,141)(123,142)
(124,143)(125,144)(126,145)(127,146)(128,147)(129,148)(130,149)(131,150)
(132,151)(133,152)(172,191)(173,192)(174,193)(175,194)(176,195)(177,196)
(178,197)(179,198)(180,199)(181,200)(182,201)(183,202)(184,203)(185,204)
(186,205)(187,206)(188,207)(189,208)(190,209);
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*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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