Polytope of Type {8,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,18}*1152b
if this polytope has a name.
Group : SmallGroup(1152,153992)
Rank : 3
Schlafli Type : {8,18}
Number of vertices, edges, etc : 32, 288, 72
Order of s0s1s2 : 18
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
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 : {4,18}*576a
3-fold quotients : {8,6}*384b
6-fold quotients : {4,6}*192a
8-fold quotients : {4,18}*144b
16-fold quotients : {4,9}*72
24-fold quotients : {4,6}*48c
48-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 17)( 2, 18)( 3, 20)( 4, 19)( 5, 21)( 6, 22)( 7, 24)( 8, 23)
( 9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 29)( 14, 30)( 15, 32)( 16, 31)
( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)
( 41, 57)( 42, 58)( 43, 60)( 44, 59)( 45, 61)( 46, 62)( 47, 64)( 48, 63)
( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 85)( 70, 86)( 71, 88)( 72, 87)
( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 93)( 78, 94)( 79, 96)( 80, 95)
( 97,113)( 98,114)( 99,116)(100,115)(101,117)(102,118)(103,120)(104,119)
(105,121)(106,122)(107,124)(108,123)(109,125)(110,126)(111,128)(112,127)
(129,145)(130,146)(131,148)(132,147)(133,149)(134,150)(135,152)(136,151)
(137,153)(138,154)(139,156)(140,155)(141,157)(142,158)(143,160)(144,159)
(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)(168,183)
(169,185)(170,186)(171,188)(172,187)(173,189)(174,190)(175,192)(176,191)
(193,209)(194,210)(195,212)(196,211)(197,213)(198,214)(199,216)(200,215)
(201,217)(202,218)(203,220)(204,219)(205,221)(206,222)(207,224)(208,223)
(225,241)(226,242)(227,244)(228,243)(229,245)(230,246)(231,248)(232,247)
(233,249)(234,250)(235,252)(236,251)(237,253)(238,254)(239,256)(240,255)
(257,273)(258,274)(259,276)(260,275)(261,277)(262,278)(263,280)(264,279)
(265,281)(266,282)(267,284)(268,283)(269,285)(270,286)(271,288)(272,287);;
s1 := ( 5, 7)( 6, 8)( 9, 12)( 10, 11)( 13, 14)( 15, 16)( 17, 32)( 18, 31)
( 19, 30)( 20, 29)( 21, 26)( 22, 25)( 23, 28)( 24, 27)( 33, 65)( 34, 66)
( 35, 67)( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 76)( 42, 75)
( 43, 74)( 44, 73)( 45, 78)( 46, 77)( 47, 80)( 48, 79)( 49, 96)( 50, 95)
( 51, 94)( 52, 93)( 53, 90)( 54, 89)( 55, 92)( 56, 91)( 57, 86)( 58, 85)
( 59, 88)( 60, 87)( 61, 84)( 62, 83)( 63, 82)( 64, 81)( 97,257)( 98,258)
( 99,259)(100,260)(101,263)(102,264)(103,261)(104,262)(105,268)(106,267)
(107,266)(108,265)(109,270)(110,269)(111,272)(112,271)(113,288)(114,287)
(115,286)(116,285)(117,282)(118,281)(119,284)(120,283)(121,278)(122,277)
(123,280)(124,279)(125,276)(126,275)(127,274)(128,273)(129,225)(130,226)
(131,227)(132,228)(133,231)(134,232)(135,229)(136,230)(137,236)(138,235)
(139,234)(140,233)(141,238)(142,237)(143,240)(144,239)(145,256)(146,255)
(147,254)(148,253)(149,250)(150,249)(151,252)(152,251)(153,246)(154,245)
(155,248)(156,247)(157,244)(158,243)(159,242)(160,241)(161,193)(162,194)
(163,195)(164,196)(165,199)(166,200)(167,197)(168,198)(169,204)(170,203)
(171,202)(172,201)(173,206)(174,205)(175,208)(176,207)(177,224)(178,223)
(179,222)(180,221)(181,218)(182,217)(183,220)(184,219)(185,214)(186,213)
(187,216)(188,215)(189,212)(190,211)(191,210)(192,209);;
s2 := ( 1, 97)( 2, 98)( 3,103)( 4,104)( 5,101)( 6,102)( 7, 99)( 8,100)
( 9,121)( 10,122)( 11,127)( 12,128)( 13,125)( 14,126)( 15,123)( 16,124)
( 17,113)( 18,114)( 19,119)( 20,120)( 21,117)( 22,118)( 23,115)( 24,116)
( 25,105)( 26,106)( 27,111)( 28,112)( 29,109)( 30,110)( 31,107)( 32,108)
( 33,161)( 34,162)( 35,167)( 36,168)( 37,165)( 38,166)( 39,163)( 40,164)
( 41,185)( 42,186)( 43,191)( 44,192)( 45,189)( 46,190)( 47,187)( 48,188)
( 49,177)( 50,178)( 51,183)( 52,184)( 53,181)( 54,182)( 55,179)( 56,180)
( 57,169)( 58,170)( 59,175)( 60,176)( 61,173)( 62,174)( 63,171)( 64,172)
( 65,129)( 66,130)( 67,135)( 68,136)( 69,133)( 70,134)( 71,131)( 72,132)
( 73,153)( 74,154)( 75,159)( 76,160)( 77,157)( 78,158)( 79,155)( 80,156)
( 81,145)( 82,146)( 83,151)( 84,152)( 85,149)( 86,150)( 87,147)( 88,148)
( 89,137)( 90,138)( 91,143)( 92,144)( 93,141)( 94,142)( 95,139)( 96,140)
(193,257)(194,258)(195,263)(196,264)(197,261)(198,262)(199,259)(200,260)
(201,281)(202,282)(203,287)(204,288)(205,285)(206,286)(207,283)(208,284)
(209,273)(210,274)(211,279)(212,280)(213,277)(214,278)(215,275)(216,276)
(217,265)(218,266)(219,271)(220,272)(221,269)(222,270)(223,267)(224,268)
(227,231)(228,232)(233,249)(234,250)(235,255)(236,256)(237,253)(238,254)
(239,251)(240,252)(243,247)(244,248);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*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*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 1, 17)( 2, 18)( 3, 20)( 4, 19)( 5, 21)( 6, 22)( 7, 24)
( 8, 23)( 9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 29)( 14, 30)( 15, 32)
( 16, 31)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)
( 40, 55)( 41, 57)( 42, 58)( 43, 60)( 44, 59)( 45, 61)( 46, 62)( 47, 64)
( 48, 63)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 85)( 70, 86)( 71, 88)
( 72, 87)( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 93)( 78, 94)( 79, 96)
( 80, 95)( 97,113)( 98,114)( 99,116)(100,115)(101,117)(102,118)(103,120)
(104,119)(105,121)(106,122)(107,124)(108,123)(109,125)(110,126)(111,128)
(112,127)(129,145)(130,146)(131,148)(132,147)(133,149)(134,150)(135,152)
(136,151)(137,153)(138,154)(139,156)(140,155)(141,157)(142,158)(143,160)
(144,159)(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)
(168,183)(169,185)(170,186)(171,188)(172,187)(173,189)(174,190)(175,192)
(176,191)(193,209)(194,210)(195,212)(196,211)(197,213)(198,214)(199,216)
(200,215)(201,217)(202,218)(203,220)(204,219)(205,221)(206,222)(207,224)
(208,223)(225,241)(226,242)(227,244)(228,243)(229,245)(230,246)(231,248)
(232,247)(233,249)(234,250)(235,252)(236,251)(237,253)(238,254)(239,256)
(240,255)(257,273)(258,274)(259,276)(260,275)(261,277)(262,278)(263,280)
(264,279)(265,281)(266,282)(267,284)(268,283)(269,285)(270,286)(271,288)
(272,287);
s1 := Sym(288)!( 5, 7)( 6, 8)( 9, 12)( 10, 11)( 13, 14)( 15, 16)( 17, 32)
( 18, 31)( 19, 30)( 20, 29)( 21, 26)( 22, 25)( 23, 28)( 24, 27)( 33, 65)
( 34, 66)( 35, 67)( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 76)
( 42, 75)( 43, 74)( 44, 73)( 45, 78)( 46, 77)( 47, 80)( 48, 79)( 49, 96)
( 50, 95)( 51, 94)( 52, 93)( 53, 90)( 54, 89)( 55, 92)( 56, 91)( 57, 86)
( 58, 85)( 59, 88)( 60, 87)( 61, 84)( 62, 83)( 63, 82)( 64, 81)( 97,257)
( 98,258)( 99,259)(100,260)(101,263)(102,264)(103,261)(104,262)(105,268)
(106,267)(107,266)(108,265)(109,270)(110,269)(111,272)(112,271)(113,288)
(114,287)(115,286)(116,285)(117,282)(118,281)(119,284)(120,283)(121,278)
(122,277)(123,280)(124,279)(125,276)(126,275)(127,274)(128,273)(129,225)
(130,226)(131,227)(132,228)(133,231)(134,232)(135,229)(136,230)(137,236)
(138,235)(139,234)(140,233)(141,238)(142,237)(143,240)(144,239)(145,256)
(146,255)(147,254)(148,253)(149,250)(150,249)(151,252)(152,251)(153,246)
(154,245)(155,248)(156,247)(157,244)(158,243)(159,242)(160,241)(161,193)
(162,194)(163,195)(164,196)(165,199)(166,200)(167,197)(168,198)(169,204)
(170,203)(171,202)(172,201)(173,206)(174,205)(175,208)(176,207)(177,224)
(178,223)(179,222)(180,221)(181,218)(182,217)(183,220)(184,219)(185,214)
(186,213)(187,216)(188,215)(189,212)(190,211)(191,210)(192,209);
s2 := Sym(288)!( 1, 97)( 2, 98)( 3,103)( 4,104)( 5,101)( 6,102)( 7, 99)
( 8,100)( 9,121)( 10,122)( 11,127)( 12,128)( 13,125)( 14,126)( 15,123)
( 16,124)( 17,113)( 18,114)( 19,119)( 20,120)( 21,117)( 22,118)( 23,115)
( 24,116)( 25,105)( 26,106)( 27,111)( 28,112)( 29,109)( 30,110)( 31,107)
( 32,108)( 33,161)( 34,162)( 35,167)( 36,168)( 37,165)( 38,166)( 39,163)
( 40,164)( 41,185)( 42,186)( 43,191)( 44,192)( 45,189)( 46,190)( 47,187)
( 48,188)( 49,177)( 50,178)( 51,183)( 52,184)( 53,181)( 54,182)( 55,179)
( 56,180)( 57,169)( 58,170)( 59,175)( 60,176)( 61,173)( 62,174)( 63,171)
( 64,172)( 65,129)( 66,130)( 67,135)( 68,136)( 69,133)( 70,134)( 71,131)
( 72,132)( 73,153)( 74,154)( 75,159)( 76,160)( 77,157)( 78,158)( 79,155)
( 80,156)( 81,145)( 82,146)( 83,151)( 84,152)( 85,149)( 86,150)( 87,147)
( 88,148)( 89,137)( 90,138)( 91,143)( 92,144)( 93,141)( 94,142)( 95,139)
( 96,140)(193,257)(194,258)(195,263)(196,264)(197,261)(198,262)(199,259)
(200,260)(201,281)(202,282)(203,287)(204,288)(205,285)(206,286)(207,283)
(208,284)(209,273)(210,274)(211,279)(212,280)(213,277)(214,278)(215,275)
(216,276)(217,265)(218,266)(219,271)(220,272)(221,269)(222,270)(223,267)
(224,268)(227,231)(228,232)(233,249)(234,250)(235,255)(236,256)(237,253)
(238,254)(239,251)(240,252)(243,247)(244,248);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*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*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope