Polytope of Type {2,4,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,36}*1152b
if this polytope has a name.
Group : SmallGroup(1152,155400)
Rank : 4
Schlafli Type : {2,4,36}
Number of vertices, edges, etc : 2, 8, 144, 72
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 : {2,4,36}*576b, {2,4,36}*576c, {2,4,18}*576
   3-fold quotients : {2,4,12}*384b
   4-fold quotients : {2,2,36}*288, {2,4,9}*288, {2,4,18}*288b, {2,4,18}*288c
   6-fold quotients : {2,4,12}*192b, {2,4,12}*192c, {2,4,6}*192
   8-fold quotients : {2,4,9}*144, {2,2,18}*144
   12-fold quotients : {2,2,12}*96, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   16-fold quotients : {2,2,9}*72
   24-fold quotients : {2,4,3}*48, {2,2,6}*48
   36-fold quotients : {2,2,4}*32
   48-fold quotients : {2,2,3}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  3,149)(  4,150)(  5,147)(  6,148)(  7,153)(  8,154)(  9,151)( 10,152)
( 11,157)( 12,158)( 13,155)( 14,156)( 15,161)( 16,162)( 17,159)( 18,160)
( 19,165)( 20,166)( 21,163)( 22,164)( 23,169)( 24,170)( 25,167)( 26,168)
( 27,173)( 28,174)( 29,171)( 30,172)( 31,177)( 32,178)( 33,175)( 34,176)
( 35,181)( 36,182)( 37,179)( 38,180)( 39,185)( 40,186)( 41,183)( 42,184)
( 43,189)( 44,190)( 45,187)( 46,188)( 47,193)( 48,194)( 49,191)( 50,192)
( 51,197)( 52,198)( 53,195)( 54,196)( 55,201)( 56,202)( 57,199)( 58,200)
( 59,205)( 60,206)( 61,203)( 62,204)( 63,209)( 64,210)( 65,207)( 66,208)
( 67,213)( 68,214)( 69,211)( 70,212)( 71,217)( 72,218)( 73,215)( 74,216)
( 75,221)( 76,222)( 77,219)( 78,220)( 79,225)( 80,226)( 81,223)( 82,224)
( 83,229)( 84,230)( 85,227)( 86,228)( 87,233)( 88,234)( 89,231)( 90,232)
( 91,237)( 92,238)( 93,235)( 94,236)( 95,241)( 96,242)( 97,239)( 98,240)
( 99,245)(100,246)(101,243)(102,244)(103,249)(104,250)(105,247)(106,248)
(107,253)(108,254)(109,251)(110,252)(111,257)(112,258)(113,255)(114,256)
(115,261)(116,262)(117,259)(118,260)(119,265)(120,266)(121,263)(122,264)
(123,269)(124,270)(125,267)(126,268)(127,273)(128,274)(129,271)(130,272)
(131,277)(132,278)(133,275)(134,276)(135,281)(136,282)(137,279)(138,280)
(139,285)(140,286)(141,283)(142,284)(143,289)(144,290)(145,287)(146,288);;
s2 := (  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);;
s3 := (  3, 99)(  4,102)(  5,101)(  6,100)(  7,107)(  8,110)(  9,109)( 10,108)
( 11,103)( 12,106)( 13,105)( 14,104)( 15, 87)( 16, 90)( 17, 89)( 18, 88)
( 19, 95)( 20, 98)( 21, 97)( 22, 96)( 23, 91)( 24, 94)( 25, 93)( 26, 92)
( 27, 75)( 28, 78)( 29, 77)( 30, 76)( 31, 83)( 32, 86)( 33, 85)( 34, 84)
( 35, 79)( 36, 82)( 37, 81)( 38, 80)( 39,135)( 40,138)( 41,137)( 42,136)
( 43,143)( 44,146)( 45,145)( 46,144)( 47,139)( 48,142)( 49,141)( 50,140)
( 51,123)( 52,126)( 53,125)( 54,124)( 55,131)( 56,134)( 57,133)( 58,132)
( 59,127)( 60,130)( 61,129)( 62,128)( 63,111)( 64,114)( 65,113)( 66,112)
( 67,119)( 68,122)( 69,121)( 70,120)( 71,115)( 72,118)( 73,117)( 74,116)
(147,243)(148,246)(149,245)(150,244)(151,251)(152,254)(153,253)(154,252)
(155,247)(156,250)(157,249)(158,248)(159,231)(160,234)(161,233)(162,232)
(163,239)(164,242)(165,241)(166,240)(167,235)(168,238)(169,237)(170,236)
(171,219)(172,222)(173,221)(174,220)(175,227)(176,230)(177,229)(178,228)
(179,223)(180,226)(181,225)(182,224)(183,279)(184,282)(185,281)(186,280)
(187,287)(188,290)(189,289)(190,288)(191,283)(192,286)(193,285)(194,284)
(195,267)(196,270)(197,269)(198,268)(199,275)(200,278)(201,277)(202,276)
(203,271)(204,274)(205,273)(206,272)(207,255)(208,258)(209,257)(210,256)
(211,263)(212,266)(213,265)(214,264)(215,259)(216,262)(217,261)(218,260);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
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(290)!(1,2);
s1 := Sym(290)!(  3,149)(  4,150)(  5,147)(  6,148)(  7,153)(  8,154)(  9,151)
( 10,152)( 11,157)( 12,158)( 13,155)( 14,156)( 15,161)( 16,162)( 17,159)
( 18,160)( 19,165)( 20,166)( 21,163)( 22,164)( 23,169)( 24,170)( 25,167)
( 26,168)( 27,173)( 28,174)( 29,171)( 30,172)( 31,177)( 32,178)( 33,175)
( 34,176)( 35,181)( 36,182)( 37,179)( 38,180)( 39,185)( 40,186)( 41,183)
( 42,184)( 43,189)( 44,190)( 45,187)( 46,188)( 47,193)( 48,194)( 49,191)
( 50,192)( 51,197)( 52,198)( 53,195)( 54,196)( 55,201)( 56,202)( 57,199)
( 58,200)( 59,205)( 60,206)( 61,203)( 62,204)( 63,209)( 64,210)( 65,207)
( 66,208)( 67,213)( 68,214)( 69,211)( 70,212)( 71,217)( 72,218)( 73,215)
( 74,216)( 75,221)( 76,222)( 77,219)( 78,220)( 79,225)( 80,226)( 81,223)
( 82,224)( 83,229)( 84,230)( 85,227)( 86,228)( 87,233)( 88,234)( 89,231)
( 90,232)( 91,237)( 92,238)( 93,235)( 94,236)( 95,241)( 96,242)( 97,239)
( 98,240)( 99,245)(100,246)(101,243)(102,244)(103,249)(104,250)(105,247)
(106,248)(107,253)(108,254)(109,251)(110,252)(111,257)(112,258)(113,255)
(114,256)(115,261)(116,262)(117,259)(118,260)(119,265)(120,266)(121,263)
(122,264)(123,269)(124,270)(125,267)(126,268)(127,273)(128,274)(129,271)
(130,272)(131,277)(132,278)(133,275)(134,276)(135,281)(136,282)(137,279)
(138,280)(139,285)(140,286)(141,283)(142,284)(143,289)(144,290)(145,287)
(146,288);
s2 := 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);
s3 := Sym(290)!(  3, 99)(  4,102)(  5,101)(  6,100)(  7,107)(  8,110)(  9,109)
( 10,108)( 11,103)( 12,106)( 13,105)( 14,104)( 15, 87)( 16, 90)( 17, 89)
( 18, 88)( 19, 95)( 20, 98)( 21, 97)( 22, 96)( 23, 91)( 24, 94)( 25, 93)
( 26, 92)( 27, 75)( 28, 78)( 29, 77)( 30, 76)( 31, 83)( 32, 86)( 33, 85)
( 34, 84)( 35, 79)( 36, 82)( 37, 81)( 38, 80)( 39,135)( 40,138)( 41,137)
( 42,136)( 43,143)( 44,146)( 45,145)( 46,144)( 47,139)( 48,142)( 49,141)
( 50,140)( 51,123)( 52,126)( 53,125)( 54,124)( 55,131)( 56,134)( 57,133)
( 58,132)( 59,127)( 60,130)( 61,129)( 62,128)( 63,111)( 64,114)( 65,113)
( 66,112)( 67,119)( 68,122)( 69,121)( 70,120)( 71,115)( 72,118)( 73,117)
( 74,116)(147,243)(148,246)(149,245)(150,244)(151,251)(152,254)(153,253)
(154,252)(155,247)(156,250)(157,249)(158,248)(159,231)(160,234)(161,233)
(162,232)(163,239)(164,242)(165,241)(166,240)(167,235)(168,238)(169,237)
(170,236)(171,219)(172,222)(173,221)(174,220)(175,227)(176,230)(177,229)
(178,228)(179,223)(180,226)(181,225)(182,224)(183,279)(184,282)(185,281)
(186,280)(187,287)(188,290)(189,289)(190,288)(191,283)(192,286)(193,285)
(194,284)(195,267)(196,270)(197,269)(198,268)(199,275)(200,278)(201,277)
(202,276)(203,271)(204,274)(205,273)(206,272)(207,255)(208,258)(209,257)
(210,256)(211,263)(212,266)(213,265)(214,264)(215,259)(216,262)(217,261)
(218,260);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
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 >;

to this polytope