Polytope of Type {2,36,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,36,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,155400)
Rank : 4
Schlafli Type : {2,36,4}
Number of vertices, edges, etc : 2, 72, 144, 8
Order of s0s1s2s3 : 36
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 : {2,36,4}*576b, {2,36,4}*576c, {2,18,4}*576
3-fold quotients : {2,12,4}*384b
4-fold quotients : {2,36,2}*288, {2,9,4}*288, {2,18,4}*288b, {2,18,4}*288c
6-fold quotients : {2,12,4}*192b, {2,12,4}*192c, {2,6,4}*192
8-fold quotients : {2,9,4}*144, {2,18,2}*144
12-fold quotients : {2,12,2}*96, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
16-fold quotients : {2,9,2}*72
24-fold quotients : {2,3,4}*48, {2,6,2}*48
36-fold quotients : {2,4,2}*32
48-fold quotients : {2,3,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 15, 35)( 16, 37)( 17, 36)
( 18, 38)( 19, 31)( 20, 33)( 21, 32)( 22, 34)( 23, 27)( 24, 29)( 25, 28)
( 26, 30)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 51, 71)( 52, 73)
( 53, 72)( 54, 74)( 55, 67)( 56, 69)( 57, 68)( 58, 70)( 59, 63)( 60, 65)
( 61, 64)( 62, 66)( 75,111)( 76,113)( 77,112)( 78,114)( 79,119)( 80,121)
( 81,120)( 82,122)( 83,115)( 84,117)( 85,116)( 86,118)( 87,143)( 88,145)
( 89,144)( 90,146)( 91,139)( 92,141)( 93,140)( 94,142)( 95,135)( 96,137)
( 97,136)( 98,138)( 99,131)(100,133)(101,132)(102,134)(103,127)(104,129)
(105,128)(106,130)(107,123)(108,125)(109,124)(110,126)(148,149)(151,155)
(152,157)(153,156)(154,158)(159,179)(160,181)(161,180)(162,182)(163,175)
(164,177)(165,176)(166,178)(167,171)(168,173)(169,172)(170,174)(184,185)
(187,191)(188,193)(189,192)(190,194)(195,215)(196,217)(197,216)(198,218)
(199,211)(200,213)(201,212)(202,214)(203,207)(204,209)(205,208)(206,210)
(219,255)(220,257)(221,256)(222,258)(223,263)(224,265)(225,264)(226,266)
(227,259)(228,261)(229,260)(230,262)(231,287)(232,289)(233,288)(234,290)
(235,283)(236,285)(237,284)(238,286)(239,279)(240,281)(241,280)(242,282)
(243,275)(244,277)(245,276)(246,278)(247,271)(248,273)(249,272)(250,274)
(251,267)(252,269)(253,268)(254,270);;
s2 := ( 3, 87)( 4, 88)( 5, 90)( 6, 89)( 7, 95)( 8, 96)( 9, 98)( 10, 97)
( 11, 91)( 12, 92)( 13, 94)( 14, 93)( 15, 75)( 16, 76)( 17, 78)( 18, 77)
( 19, 83)( 20, 84)( 21, 86)( 22, 85)( 23, 79)( 24, 80)( 25, 82)( 26, 81)
( 27,107)( 28,108)( 29,110)( 30,109)( 31,103)( 32,104)( 33,106)( 34,105)
( 35, 99)( 36,100)( 37,102)( 38,101)( 39,123)( 40,124)( 41,126)( 42,125)
( 43,131)( 44,132)( 45,134)( 46,133)( 47,127)( 48,128)( 49,130)( 50,129)
( 51,111)( 52,112)( 53,114)( 54,113)( 55,119)( 56,120)( 57,122)( 58,121)
( 59,115)( 60,116)( 61,118)( 62,117)( 63,143)( 64,144)( 65,146)( 66,145)
( 67,139)( 68,140)( 69,142)( 70,141)( 71,135)( 72,136)( 73,138)( 74,137)
(147,231)(148,232)(149,234)(150,233)(151,239)(152,240)(153,242)(154,241)
(155,235)(156,236)(157,238)(158,237)(159,219)(160,220)(161,222)(162,221)
(163,227)(164,228)(165,230)(166,229)(167,223)(168,224)(169,226)(170,225)
(171,251)(172,252)(173,254)(174,253)(175,247)(176,248)(177,250)(178,249)
(179,243)(180,244)(181,246)(182,245)(183,267)(184,268)(185,270)(186,269)
(187,275)(188,276)(189,278)(190,277)(191,271)(192,272)(193,274)(194,273)
(195,255)(196,256)(197,258)(198,257)(199,263)(200,264)(201,266)(202,265)
(203,259)(204,260)(205,262)(206,261)(207,287)(208,288)(209,290)(210,289)
(211,283)(212,284)(213,286)(214,285)(215,279)(216,280)(217,282)(218,281);;
s3 := ( 3,150)( 4,149)( 5,148)( 6,147)( 7,154)( 8,153)( 9,152)( 10,151)
( 11,158)( 12,157)( 13,156)( 14,155)( 15,162)( 16,161)( 17,160)( 18,159)
( 19,166)( 20,165)( 21,164)( 22,163)( 23,170)( 24,169)( 25,168)( 26,167)
( 27,174)( 28,173)( 29,172)( 30,171)( 31,178)( 32,177)( 33,176)( 34,175)
( 35,182)( 36,181)( 37,180)( 38,179)( 39,186)( 40,185)( 41,184)( 42,183)
( 43,190)( 44,189)( 45,188)( 46,187)( 47,194)( 48,193)( 49,192)( 50,191)
( 51,198)( 52,197)( 53,196)( 54,195)( 55,202)( 56,201)( 57,200)( 58,199)
( 59,206)( 60,205)( 61,204)( 62,203)( 63,210)( 64,209)( 65,208)( 66,207)
( 67,214)( 68,213)( 69,212)( 70,211)( 71,218)( 72,217)( 73,216)( 74,215)
( 75,222)( 76,221)( 77,220)( 78,219)( 79,226)( 80,225)( 81,224)( 82,223)
( 83,230)( 84,229)( 85,228)( 86,227)( 87,234)( 88,233)( 89,232)( 90,231)
( 91,238)( 92,237)( 93,236)( 94,235)( 95,242)( 96,241)( 97,240)( 98,239)
( 99,246)(100,245)(101,244)(102,243)(103,250)(104,249)(105,248)(106,247)
(107,254)(108,253)(109,252)(110,251)(111,258)(112,257)(113,256)(114,255)
(115,262)(116,261)(117,260)(118,259)(119,266)(120,265)(121,264)(122,263)
(123,270)(124,269)(125,268)(126,267)(127,274)(128,273)(129,272)(130,271)
(131,278)(132,277)(133,276)(134,275)(135,282)(136,281)(137,280)(138,279)
(139,286)(140,285)(141,284)(142,283)(143,290)(144,289)(145,288)(146,287);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*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*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(290)!(1,2);
s1 := Sym(290)!( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 15, 35)( 16, 37)
( 17, 36)( 18, 38)( 19, 31)( 20, 33)( 21, 32)( 22, 34)( 23, 27)( 24, 29)
( 25, 28)( 26, 30)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 51, 71)
( 52, 73)( 53, 72)( 54, 74)( 55, 67)( 56, 69)( 57, 68)( 58, 70)( 59, 63)
( 60, 65)( 61, 64)( 62, 66)( 75,111)( 76,113)( 77,112)( 78,114)( 79,119)
( 80,121)( 81,120)( 82,122)( 83,115)( 84,117)( 85,116)( 86,118)( 87,143)
( 88,145)( 89,144)( 90,146)( 91,139)( 92,141)( 93,140)( 94,142)( 95,135)
( 96,137)( 97,136)( 98,138)( 99,131)(100,133)(101,132)(102,134)(103,127)
(104,129)(105,128)(106,130)(107,123)(108,125)(109,124)(110,126)(148,149)
(151,155)(152,157)(153,156)(154,158)(159,179)(160,181)(161,180)(162,182)
(163,175)(164,177)(165,176)(166,178)(167,171)(168,173)(169,172)(170,174)
(184,185)(187,191)(188,193)(189,192)(190,194)(195,215)(196,217)(197,216)
(198,218)(199,211)(200,213)(201,212)(202,214)(203,207)(204,209)(205,208)
(206,210)(219,255)(220,257)(221,256)(222,258)(223,263)(224,265)(225,264)
(226,266)(227,259)(228,261)(229,260)(230,262)(231,287)(232,289)(233,288)
(234,290)(235,283)(236,285)(237,284)(238,286)(239,279)(240,281)(241,280)
(242,282)(243,275)(244,277)(245,276)(246,278)(247,271)(248,273)(249,272)
(250,274)(251,267)(252,269)(253,268)(254,270);
s2 := Sym(290)!( 3, 87)( 4, 88)( 5, 90)( 6, 89)( 7, 95)( 8, 96)( 9, 98)
( 10, 97)( 11, 91)( 12, 92)( 13, 94)( 14, 93)( 15, 75)( 16, 76)( 17, 78)
( 18, 77)( 19, 83)( 20, 84)( 21, 86)( 22, 85)( 23, 79)( 24, 80)( 25, 82)
( 26, 81)( 27,107)( 28,108)( 29,110)( 30,109)( 31,103)( 32,104)( 33,106)
( 34,105)( 35, 99)( 36,100)( 37,102)( 38,101)( 39,123)( 40,124)( 41,126)
( 42,125)( 43,131)( 44,132)( 45,134)( 46,133)( 47,127)( 48,128)( 49,130)
( 50,129)( 51,111)( 52,112)( 53,114)( 54,113)( 55,119)( 56,120)( 57,122)
( 58,121)( 59,115)( 60,116)( 61,118)( 62,117)( 63,143)( 64,144)( 65,146)
( 66,145)( 67,139)( 68,140)( 69,142)( 70,141)( 71,135)( 72,136)( 73,138)
( 74,137)(147,231)(148,232)(149,234)(150,233)(151,239)(152,240)(153,242)
(154,241)(155,235)(156,236)(157,238)(158,237)(159,219)(160,220)(161,222)
(162,221)(163,227)(164,228)(165,230)(166,229)(167,223)(168,224)(169,226)
(170,225)(171,251)(172,252)(173,254)(174,253)(175,247)(176,248)(177,250)
(178,249)(179,243)(180,244)(181,246)(182,245)(183,267)(184,268)(185,270)
(186,269)(187,275)(188,276)(189,278)(190,277)(191,271)(192,272)(193,274)
(194,273)(195,255)(196,256)(197,258)(198,257)(199,263)(200,264)(201,266)
(202,265)(203,259)(204,260)(205,262)(206,261)(207,287)(208,288)(209,290)
(210,289)(211,283)(212,284)(213,286)(214,285)(215,279)(216,280)(217,282)
(218,281);
s3 := Sym(290)!( 3,150)( 4,149)( 5,148)( 6,147)( 7,154)( 8,153)( 9,152)
( 10,151)( 11,158)( 12,157)( 13,156)( 14,155)( 15,162)( 16,161)( 17,160)
( 18,159)( 19,166)( 20,165)( 21,164)( 22,163)( 23,170)( 24,169)( 25,168)
( 26,167)( 27,174)( 28,173)( 29,172)( 30,171)( 31,178)( 32,177)( 33,176)
( 34,175)( 35,182)( 36,181)( 37,180)( 38,179)( 39,186)( 40,185)( 41,184)
( 42,183)( 43,190)( 44,189)( 45,188)( 46,187)( 47,194)( 48,193)( 49,192)
( 50,191)( 51,198)( 52,197)( 53,196)( 54,195)( 55,202)( 56,201)( 57,200)
( 58,199)( 59,206)( 60,205)( 61,204)( 62,203)( 63,210)( 64,209)( 65,208)
( 66,207)( 67,214)( 68,213)( 69,212)( 70,211)( 71,218)( 72,217)( 73,216)
( 74,215)( 75,222)( 76,221)( 77,220)( 78,219)( 79,226)( 80,225)( 81,224)
( 82,223)( 83,230)( 84,229)( 85,228)( 86,227)( 87,234)( 88,233)( 89,232)
( 90,231)( 91,238)( 92,237)( 93,236)( 94,235)( 95,242)( 96,241)( 97,240)
( 98,239)( 99,246)(100,245)(101,244)(102,243)(103,250)(104,249)(105,248)
(106,247)(107,254)(108,253)(109,252)(110,251)(111,258)(112,257)(113,256)
(114,255)(115,262)(116,261)(117,260)(118,259)(119,266)(120,265)(121,264)
(122,263)(123,270)(124,269)(125,268)(126,267)(127,274)(128,273)(129,272)
(130,271)(131,278)(132,277)(133,276)(134,275)(135,282)(136,281)(137,280)
(138,279)(139,286)(140,285)(141,284)(142,283)(143,290)(144,289)(145,288)
(146,287);
poly := sub<Sym(290)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s1*s2*s3*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*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope