Polytope of Type {18,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,8}*1152c
if this polytope has a name.
Group : SmallGroup(1152,153992)
Rank : 3
Schlafli Type : {18,8}
Number of vertices, edges, etc : 72, 288, 32
Order of s₀s₁s₂ : 18
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
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}*576a
   3-fold quotients : {6,8}*384c
   6-fold quotients : {6,4}*192a
   8-fold quotients : {18,4}*144b
   16-fold quotients : {9,4}*72
   24-fold quotients : {6,4}*48c
   48-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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