Polytope of Type {6,4,38}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,38}*1824
Also Known As : {{6,4|2},{4,38|2}}. if this polytope has another name.
Group : SmallGroup(1824,1141)
Rank : 4
Schlafli Type : {6,4,38}
Number of vertices, edges, etc : 6, 12, 76, 38
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 : {6,2,38}*912
3-fold quotients : {2,4,38}*608
4-fold quotients : {3,2,38}*456, {6,2,19}*456
6-fold quotients : {2,2,38}*304
8-fold quotients : {3,2,19}*228
12-fold quotients : {2,2,19}*152
19-fold quotients : {6,4,2}*96a
38-fold quotients : {6,2,2}*48
57-fold quotients : {2,4,2}*32
76-fold quotients : {3,2,2}*24
114-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
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)(134,153)(135,154)
(136,155)(137,156)(138,157)(139,158)(140,159)(141,160)(142,161)(143,162)
(144,163)(145,164)(146,165)(147,166)(148,167)(149,168)(150,169)(151,170)
(152,171)(191,210)(192,211)(193,212)(194,213)(195,214)(196,215)(197,216)
(198,217)(199,218)(200,219)(201,220)(202,221)(203,222)(204,223)(205,224)
(206,225)(207,226)(208,227)(209,228);;
s1 := ( 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);;
s2 := ( 1,115)( 2,133)( 3,132)( 4,131)( 5,130)( 6,129)( 7,128)( 8,127)
( 9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,120)( 16,119)
( 17,118)( 18,117)( 19,116)( 20,134)( 21,152)( 22,151)( 23,150)( 24,149)
( 25,148)( 26,147)( 27,146)( 28,145)( 29,144)( 30,143)( 31,142)( 32,141)
( 33,140)( 34,139)( 35,138)( 36,137)( 37,136)( 38,135)( 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)( 58,172)( 59,190)( 60,189)( 61,188)( 62,187)( 63,186)( 64,185)
( 65,184)( 66,183)( 67,182)( 68,181)( 69,180)( 70,179)( 71,178)( 72,177)
( 73,176)( 74,175)( 75,174)( 76,173)( 77,191)( 78,209)( 79,208)( 80,207)
( 81,206)( 82,205)( 83,204)( 84,203)( 85,202)( 86,201)( 87,200)( 88,199)
( 89,198)( 90,197)( 91,196)( 92,195)( 93,194)( 94,193)( 95,192)( 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);;
s3 := ( 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,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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)(134,153)
(135,154)(136,155)(137,156)(138,157)(139,158)(140,159)(141,160)(142,161)
(143,162)(144,163)(145,164)(146,165)(147,166)(148,167)(149,168)(150,169)
(151,170)(152,171)(191,210)(192,211)(193,212)(194,213)(195,214)(196,215)
(197,216)(198,217)(199,218)(200,219)(201,220)(202,221)(203,222)(204,223)
(205,224)(206,225)(207,226)(208,227)(209,228);
s1 := 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);
s2 := Sym(228)!( 1,115)( 2,133)( 3,132)( 4,131)( 5,130)( 6,129)( 7,128)
( 8,127)( 9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,120)
( 16,119)( 17,118)( 18,117)( 19,116)( 20,134)( 21,152)( 22,151)( 23,150)
( 24,149)( 25,148)( 26,147)( 27,146)( 28,145)( 29,144)( 30,143)( 31,142)
( 32,141)( 33,140)( 34,139)( 35,138)( 36,137)( 37,136)( 38,135)( 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)( 58,172)( 59,190)( 60,189)( 61,188)( 62,187)( 63,186)
( 64,185)( 65,184)( 66,183)( 67,182)( 68,181)( 69,180)( 70,179)( 71,178)
( 72,177)( 73,176)( 74,175)( 75,174)( 76,173)( 77,191)( 78,209)( 79,208)
( 80,207)( 81,206)( 82,205)( 83,204)( 84,203)( 85,202)( 86,201)( 87,200)
( 88,199)( 89,198)( 90,197)( 91,196)( 92,195)( 93,194)( 94,193)( 95,192)
( 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);
s3 := 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,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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope