Polytope of Type {288}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {288}*576
Also Known As : 288-gon, {288}. if this polytope has another name.
Group : SmallGroup(576,7)
Rank : 2
Schlafli Type : {288}
Number of vertices, edges, etc : 288, 288
Order of s0s1 : 288
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{288,2} of size 1152
Vertex Figure Of :
{2,288} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {144}*288
3-fold quotients : {96}*192
4-fold quotients : {72}*144
6-fold quotients : {48}*96
8-fold quotients : {36}*72
9-fold quotients : {32}*64
12-fold quotients : {24}*48
16-fold quotients : {18}*36
18-fold quotients : {16}*32
24-fold quotients : {12}*24
32-fold quotients : {9}*18
36-fold quotients : {8}*16
48-fold quotients : {6}*12
72-fold quotients : {4}*8
96-fold quotients : {3}*6
144-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {576}*1152
3-fold covers : {864}*1728
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 8)( 5, 7)( 6, 9)( 11, 12)( 13, 17)( 14, 16)( 15, 18)
( 19, 28)( 20, 30)( 21, 29)( 22, 35)( 23, 34)( 24, 36)( 25, 32)( 26, 31)
( 27, 33)( 37, 55)( 38, 57)( 39, 56)( 40, 62)( 41, 61)( 42, 63)( 43, 59)
( 44, 58)( 45, 60)( 46, 64)( 47, 66)( 48, 65)( 49, 71)( 50, 70)( 51, 72)
( 52, 68)( 53, 67)( 54, 69)( 73,109)( 74,111)( 75,110)( 76,116)( 77,115)
( 78,117)( 79,113)( 80,112)( 81,114)( 82,118)( 83,120)( 84,119)( 85,125)
( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)( 91,136)( 92,138)( 93,137)
( 94,143)( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,127)(101,129)
(102,128)(103,134)(104,133)(105,135)(106,131)(107,130)(108,132)(145,217)
(146,219)(147,218)(148,224)(149,223)(150,225)(151,221)(152,220)(153,222)
(154,226)(155,228)(156,227)(157,233)(158,232)(159,234)(160,230)(161,229)
(162,231)(163,244)(164,246)(165,245)(166,251)(167,250)(168,252)(169,248)
(170,247)(171,249)(172,235)(173,237)(174,236)(175,242)(176,241)(177,243)
(178,239)(179,238)(180,240)(181,271)(182,273)(183,272)(184,278)(185,277)
(186,279)(187,275)(188,274)(189,276)(190,280)(191,282)(192,281)(193,287)
(194,286)(195,288)(196,284)(197,283)(198,285)(199,253)(200,255)(201,254)
(202,260)(203,259)(204,261)(205,257)(206,256)(207,258)(208,262)(209,264)
(210,263)(211,269)(212,268)(213,270)(214,266)(215,265)(216,267);;
s1 := ( 1,148)( 2,150)( 3,149)( 4,145)( 5,147)( 6,146)( 7,152)( 8,151)
( 9,153)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)( 16,161)
( 17,160)( 18,162)( 19,175)( 20,177)( 21,176)( 22,172)( 23,174)( 24,173)
( 25,179)( 26,178)( 27,180)( 28,166)( 29,168)( 30,167)( 31,163)( 32,165)
( 33,164)( 34,170)( 35,169)( 36,171)( 37,202)( 38,204)( 39,203)( 40,199)
( 41,201)( 42,200)( 43,206)( 44,205)( 45,207)( 46,211)( 47,213)( 48,212)
( 49,208)( 50,210)( 51,209)( 52,215)( 53,214)( 54,216)( 55,184)( 56,186)
( 57,185)( 58,181)( 59,183)( 60,182)( 61,188)( 62,187)( 63,189)( 64,193)
( 65,195)( 66,194)( 67,190)( 68,192)( 69,191)( 70,197)( 71,196)( 72,198)
( 73,256)( 74,258)( 75,257)( 76,253)( 77,255)( 78,254)( 79,260)( 80,259)
( 81,261)( 82,265)( 83,267)( 84,266)( 85,262)( 86,264)( 87,263)( 88,269)
( 89,268)( 90,270)( 91,283)( 92,285)( 93,284)( 94,280)( 95,282)( 96,281)
( 97,287)( 98,286)( 99,288)(100,274)(101,276)(102,275)(103,271)(104,273)
(105,272)(106,278)(107,277)(108,279)(109,220)(110,222)(111,221)(112,217)
(113,219)(114,218)(115,224)(116,223)(117,225)(118,229)(119,231)(120,230)
(121,226)(122,228)(123,227)(124,233)(125,232)(126,234)(127,247)(128,249)
(129,248)(130,244)(131,246)(132,245)(133,251)(134,250)(135,252)(136,238)
(137,240)(138,239)(139,235)(140,237)(141,236)(142,242)(143,241)(144,243);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 2, 3)( 4, 8)( 5, 7)( 6, 9)( 11, 12)( 13, 17)( 14, 16)
( 15, 18)( 19, 28)( 20, 30)( 21, 29)( 22, 35)( 23, 34)( 24, 36)( 25, 32)
( 26, 31)( 27, 33)( 37, 55)( 38, 57)( 39, 56)( 40, 62)( 41, 61)( 42, 63)
( 43, 59)( 44, 58)( 45, 60)( 46, 64)( 47, 66)( 48, 65)( 49, 71)( 50, 70)
( 51, 72)( 52, 68)( 53, 67)( 54, 69)( 73,109)( 74,111)( 75,110)( 76,116)
( 77,115)( 78,117)( 79,113)( 80,112)( 81,114)( 82,118)( 83,120)( 84,119)
( 85,125)( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)( 91,136)( 92,138)
( 93,137)( 94,143)( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,127)
(101,129)(102,128)(103,134)(104,133)(105,135)(106,131)(107,130)(108,132)
(145,217)(146,219)(147,218)(148,224)(149,223)(150,225)(151,221)(152,220)
(153,222)(154,226)(155,228)(156,227)(157,233)(158,232)(159,234)(160,230)
(161,229)(162,231)(163,244)(164,246)(165,245)(166,251)(167,250)(168,252)
(169,248)(170,247)(171,249)(172,235)(173,237)(174,236)(175,242)(176,241)
(177,243)(178,239)(179,238)(180,240)(181,271)(182,273)(183,272)(184,278)
(185,277)(186,279)(187,275)(188,274)(189,276)(190,280)(191,282)(192,281)
(193,287)(194,286)(195,288)(196,284)(197,283)(198,285)(199,253)(200,255)
(201,254)(202,260)(203,259)(204,261)(205,257)(206,256)(207,258)(208,262)
(209,264)(210,263)(211,269)(212,268)(213,270)(214,266)(215,265)(216,267);
s1 := Sym(288)!( 1,148)( 2,150)( 3,149)( 4,145)( 5,147)( 6,146)( 7,152)
( 8,151)( 9,153)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)
( 16,161)( 17,160)( 18,162)( 19,175)( 20,177)( 21,176)( 22,172)( 23,174)
( 24,173)( 25,179)( 26,178)( 27,180)( 28,166)( 29,168)( 30,167)( 31,163)
( 32,165)( 33,164)( 34,170)( 35,169)( 36,171)( 37,202)( 38,204)( 39,203)
( 40,199)( 41,201)( 42,200)( 43,206)( 44,205)( 45,207)( 46,211)( 47,213)
( 48,212)( 49,208)( 50,210)( 51,209)( 52,215)( 53,214)( 54,216)( 55,184)
( 56,186)( 57,185)( 58,181)( 59,183)( 60,182)( 61,188)( 62,187)( 63,189)
( 64,193)( 65,195)( 66,194)( 67,190)( 68,192)( 69,191)( 70,197)( 71,196)
( 72,198)( 73,256)( 74,258)( 75,257)( 76,253)( 77,255)( 78,254)( 79,260)
( 80,259)( 81,261)( 82,265)( 83,267)( 84,266)( 85,262)( 86,264)( 87,263)
( 88,269)( 89,268)( 90,270)( 91,283)( 92,285)( 93,284)( 94,280)( 95,282)
( 96,281)( 97,287)( 98,286)( 99,288)(100,274)(101,276)(102,275)(103,271)
(104,273)(105,272)(106,278)(107,277)(108,279)(109,220)(110,222)(111,221)
(112,217)(113,219)(114,218)(115,224)(116,223)(117,225)(118,229)(119,231)
(120,230)(121,226)(122,228)(123,227)(124,233)(125,232)(126,234)(127,247)
(128,249)(129,248)(130,244)(131,246)(132,245)(133,251)(134,250)(135,252)
(136,238)(137,240)(138,239)(139,235)(140,237)(141,236)(142,242)(143,241)
(144,243);
poly := sub<Sym(288)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope