Polytope of Type {18,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,154380)
Rank : 3
Schlafli Type : {18,4}
Number of vertices, edges, etc : 144, 288, 32
Order of s₀s₁s₂ : 72
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {18,4}*576b
   3-fold quotients : {6,4}*384b
   4-fold quotients : {18,4}*288
   6-fold quotients : {6,4}*192b
   8-fold quotients : {18,4}*144a, {9,4}*144, {18,4}*144b, {18,4}*144c
   12-fold quotients : {6,4}*96
   16-fold quotients : {9,4}*72, {18,2}*72
   24-fold quotients : {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {9,2}*36
   48-fold quotients : {3,4}*24, {6,2}*24
   72-fold quotients : {2,4}*16
   96-fold quotients : {3,2}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1*s2*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