Polytope of Type {4,36,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,36,4}*1152e
if this polytope has a name.
Group : SmallGroup(1152,154208)
Rank : 4
Schlafli Type : {4,36,4}
Number of vertices, edges, etc : 4, 72, 72, 4
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-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 : {4,36,2}*576c, {4,18,4}*576c
3-fold quotients : {4,12,4}*384e
4-fold quotients : {4,18,2}*288b
6-fold quotients : {4,12,2}*192c, {4,6,4}*192c
8-fold quotients : {4,9,2}*144
12-fold quotients : {4,6,2}*96c
24-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 1, 39)( 2, 40)( 3, 37)( 4, 38)( 5, 43)( 6, 44)( 7, 41)( 8, 42)( 9, 47)( 10, 48)( 11, 45)( 12, 46)( 13, 51)( 14, 52)( 15, 49)( 16, 50)( 17, 55)( 18, 56)( 19, 53)( 20, 54)( 21, 59)( 22, 60)( 23, 57)( 24, 58)( 25, 63)( 26, 64)( 27, 61)( 28, 62)( 29, 67)( 30, 68)( 31, 65)( 32, 66)( 33, 71)( 34, 72)( 35, 69)( 36, 70)( 73,111)( 74,112)( 75,109)( 76,110)( 77,115)( 78,116)( 79,113)( 80,114)( 81,119)( 82,120)( 83,117)( 84,118)( 85,123)( 86,124)( 87,121)( 88,122)( 89,127)( 90,128)( 91,125)( 92,126)( 93,131)( 94,132)( 95,129)( 96,130)( 97,135)( 98,136)( 99,133)(100,134)(101,139)(102,140)(103,137)(104,138)(105,143)(106,144)(107,141)(108,142)(145,183)(146,184)(147,181)(148,182)(149,187)(150,188)(151,185)(152,186)(153,191)(154,192)(155,189)(156,190)(157,195)(158,196)(159,193)(160,194)(161,199)(162,200)(163,197)(164,198)(165,203)(166,204)(167,201)(168,202)(169,207)(170,208)(171,205)(172,206)(173,211)(174,212)(175,209)(176,210)(177,215)(178,216)(179,213)(180,214)(217,255)(218,256)(219,253)(220,254)(221,259)(222,260)(223,257)(224,258)(225,263)(226,264)(227,261)(228,262)(229,267)(230,268)(231,265)(232,266)(233,271)(234,272)(235,269)(236,270)(237,275)(238,276)(239,273)(240,274)(241,279)(242,280)(243,277)(244,278)(245,283)(246,284)(247,281)(248,282)(249,287)(250,288)(251,285)(252,286);;
s1 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)( 24, 27)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 69)( 50, 70)( 51, 72)( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)( 85,105)( 86,106)( 87,108)( 88,107)( 89,101)( 90,102)( 91,104)( 92,103)( 93, 97)( 94, 98)( 95,100)( 96, 99)(111,112)(113,117)(114,118)(115,120)(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(145,181)(146,182)(147,184)(148,183)(149,189)(150,190)(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,213)(158,214)(159,216)(160,215)(161,209)(162,210)(163,212)(164,211)(165,205)(166,206)(167,208)(168,207)(169,201)(170,202)(171,204)(172,203)(173,197)(174,198)(175,200)(176,199)(177,193)(178,194)(179,196)(180,195)(217,253)(218,254)(219,256)(220,255)(221,261)(222,262)(223,264)(224,263)(225,257)(226,258)(227,260)(228,259)(229,285)(230,286)(231,288)(232,287)(233,281)(234,282)(235,284)(236,283)(237,277)(238,278)(239,280)(240,279)(241,273)(242,274)(243,276)(244,275)(245,269)(246,270)(247,272)(248,271)(249,265)(250,266)(251,268)(252,267);;
s2 := ( 1,157)( 2,160)( 3,159)( 4,158)( 5,165)( 6,168)( 7,167)( 8,166)( 9,161)( 10,164)( 11,163)( 12,162)( 13,145)( 14,148)( 15,147)( 16,146)( 17,153)( 18,156)( 19,155)( 20,154)( 21,149)( 22,152)( 23,151)( 24,150)( 25,177)( 26,180)( 27,179)( 28,178)( 29,173)( 30,176)( 31,175)( 32,174)( 33,169)( 34,172)( 35,171)( 36,170)( 37,193)( 38,196)( 39,195)( 40,194)( 41,201)( 42,204)( 43,203)( 44,202)( 45,197)( 46,200)( 47,199)( 48,198)( 49,181)( 50,184)( 51,183)( 52,182)( 53,189)( 54,192)( 55,191)( 56,190)( 57,185)( 58,188)( 59,187)( 60,186)( 61,213)( 62,216)( 63,215)( 64,214)( 65,209)( 66,212)( 67,211)( 68,210)( 69,205)( 70,208)( 71,207)( 72,206)( 73,229)( 74,232)( 75,231)( 76,230)( 77,237)( 78,240)( 79,239)( 80,238)( 81,233)( 82,236)( 83,235)( 84,234)( 85,217)( 86,220)( 87,219)( 88,218)( 89,225)( 90,228)( 91,227)( 92,226)( 93,221)( 94,224)( 95,223)( 96,222)( 97,249)( 98,252)( 99,251)(100,250)(101,245)(102,248)(103,247)(104,246)(105,241)(106,244)(107,243)(108,242)(109,265)(110,268)(111,267)(112,266)(113,273)(114,276)(115,275)(116,274)(117,269)(118,272)(119,271)(120,270)(121,253)(122,256)(123,255)(124,254)(125,261)(126,264)(127,263)(128,262)(129,257)(130,260)(131,259)(132,258)(133,285)(134,288)(135,287)(136,286)(137,281)(138,284)(139,283)(140,282)(141,277)(142,280)(143,279)(144,278);;
s3 := (145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)(152,224)(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)(160,232)(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)(168,240)(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)(184,256)(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)(192,264)(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)(200,272)(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)(208,280)(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)(216,288);;
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*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s2*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 1, 39)( 2, 40)( 3, 37)( 4, 38)( 5, 43)( 6, 44)( 7, 41)( 8, 42)( 9, 47)( 10, 48)( 11, 45)( 12, 46)( 13, 51)( 14, 52)( 15, 49)( 16, 50)( 17, 55)( 18, 56)( 19, 53)( 20, 54)( 21, 59)( 22, 60)( 23, 57)( 24, 58)( 25, 63)( 26, 64)( 27, 61)( 28, 62)( 29, 67)( 30, 68)( 31, 65)( 32, 66)( 33, 71)( 34, 72)( 35, 69)( 36, 70)( 73,111)( 74,112)( 75,109)( 76,110)( 77,115)( 78,116)( 79,113)( 80,114)( 81,119)( 82,120)( 83,117)( 84,118)( 85,123)( 86,124)( 87,121)( 88,122)( 89,127)( 90,128)( 91,125)( 92,126)( 93,131)( 94,132)( 95,129)( 96,130)( 97,135)( 98,136)( 99,133)(100,134)(101,139)(102,140)(103,137)(104,138)(105,143)(106,144)(107,141)(108,142)(145,183)(146,184)(147,181)(148,182)(149,187)(150,188)(151,185)(152,186)(153,191)(154,192)(155,189)(156,190)(157,195)(158,196)(159,193)(160,194)(161,199)(162,200)(163,197)(164,198)(165,203)(166,204)(167,201)(168,202)(169,207)(170,208)(171,205)(172,206)(173,211)(174,212)(175,209)(176,210)(177,215)(178,216)(179,213)(180,214)(217,255)(218,256)(219,253)(220,254)(221,259)(222,260)(223,257)(224,258)(225,263)(226,264)(227,261)(228,262)(229,267)(230,268)(231,265)(232,266)(233,271)(234,272)(235,269)(236,270)(237,275)(238,276)(239,273)(240,274)(241,279)(242,280)(243,277)(244,278)(245,283)(246,284)(247,281)(248,282)(249,287)(250,288)(251,285)(252,286);
s1 := Sym(288)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)( 24, 27)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 69)( 50, 70)( 51, 72)( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)( 85,105)( 86,106)( 87,108)( 88,107)( 89,101)( 90,102)( 91,104)( 92,103)( 93, 97)( 94, 98)( 95,100)( 96, 99)(111,112)(113,117)(114,118)(115,120)(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(145,181)(146,182)(147,184)(148,183)(149,189)(150,190)(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,213)(158,214)(159,216)(160,215)(161,209)(162,210)(163,212)(164,211)(165,205)(166,206)(167,208)(168,207)(169,201)(170,202)(171,204)(172,203)(173,197)(174,198)(175,200)(176,199)(177,193)(178,194)(179,196)(180,195)(217,253)(218,254)(219,256)(220,255)(221,261)(222,262)(223,264)(224,263)(225,257)(226,258)(227,260)(228,259)(229,285)(230,286)(231,288)(232,287)(233,281)(234,282)(235,284)(236,283)(237,277)(238,278)(239,280)(240,279)(241,273)(242,274)(243,276)(244,275)(245,269)(246,270)(247,272)(248,271)(249,265)(250,266)(251,268)(252,267);
s2 := Sym(288)!( 1,157)( 2,160)( 3,159)( 4,158)( 5,165)( 6,168)( 7,167)( 8,166)( 9,161)( 10,164)( 11,163)( 12,162)( 13,145)( 14,148)( 15,147)( 16,146)( 17,153)( 18,156)( 19,155)( 20,154)( 21,149)( 22,152)( 23,151)( 24,150)( 25,177)( 26,180)( 27,179)( 28,178)( 29,173)( 30,176)( 31,175)( 32,174)( 33,169)( 34,172)( 35,171)( 36,170)( 37,193)( 38,196)( 39,195)( 40,194)( 41,201)( 42,204)( 43,203)( 44,202)( 45,197)( 46,200)( 47,199)( 48,198)( 49,181)( 50,184)( 51,183)( 52,182)( 53,189)( 54,192)( 55,191)( 56,190)( 57,185)( 58,188)( 59,187)( 60,186)( 61,213)( 62,216)( 63,215)( 64,214)( 65,209)( 66,212)( 67,211)( 68,210)( 69,205)( 70,208)( 71,207)( 72,206)( 73,229)( 74,232)( 75,231)( 76,230)( 77,237)( 78,240)( 79,239)( 80,238)( 81,233)( 82,236)( 83,235)( 84,234)( 85,217)( 86,220)( 87,219)( 88,218)( 89,225)( 90,228)( 91,227)( 92,226)( 93,221)( 94,224)( 95,223)( 96,222)( 97,249)( 98,252)( 99,251)(100,250)(101,245)(102,248)(103,247)(104,246)(105,241)(106,244)(107,243)(108,242)(109,265)(110,268)(111,267)(112,266)(113,273)(114,276)(115,275)(116,274)(117,269)(118,272)(119,271)(120,270)(121,253)(122,256)(123,255)(124,254)(125,261)(126,264)(127,263)(128,262)(129,257)(130,260)(131,259)(132,258)(133,285)(134,288)(135,287)(136,286)(137,281)(138,284)(139,283)(140,282)(141,277)(142,280)(143,279)(144,278);
s3 := Sym(288)!(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)(152,224)(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)(160,232)(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)(168,240)(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)(184,256)(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)(192,264)(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)(200,272)(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)(208,280)(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)(216,288);
poly := sub<Sym(288)|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*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 >;
References : None.
to this polytope