Polytope of Type {4,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,6}*1152i
if this polytope has a name.
Group : SmallGroup(1152,157852)
Rank : 4
Schlafli Type : {4,6,6}
Number of vertices, edges, etc : 16, 48, 72, 6
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 4
Special Properties :
Non-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 : {4,6,3}*576b
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)
(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)
(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)
(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288);;
s1 := ( 2, 5)( 3, 9)( 4, 13)( 7, 10)( 8, 14)( 12, 15)( 17, 33)( 18, 37)
( 19, 41)( 20, 45)( 21, 34)( 22, 38)( 23, 42)( 24, 46)( 25, 35)( 26, 39)
( 27, 43)( 28, 47)( 29, 36)( 30, 40)( 31, 44)( 32, 48)( 49, 65)( 50, 69)
( 51, 73)( 52, 77)( 53, 66)( 54, 70)( 55, 74)( 56, 78)( 57, 67)( 58, 71)
( 59, 75)( 60, 79)( 61, 68)( 62, 72)( 63, 76)( 64, 80)( 82, 85)( 83, 89)
( 84, 93)( 87, 90)( 88, 94)( 92, 95)( 97,129)( 98,133)( 99,137)(100,141)
(101,130)(102,134)(103,138)(104,142)(105,131)(106,135)(107,139)(108,143)
(109,132)(110,136)(111,140)(112,144)(114,117)(115,121)(116,125)(119,122)
(120,126)(124,127)(146,149)(147,153)(148,157)(151,154)(152,158)(156,159)
(161,177)(162,181)(163,185)(164,189)(165,178)(166,182)(167,186)(168,190)
(169,179)(170,183)(171,187)(172,191)(173,180)(174,184)(175,188)(176,192)
(193,209)(194,213)(195,217)(196,221)(197,210)(198,214)(199,218)(200,222)
(201,211)(202,215)(203,219)(204,223)(205,212)(206,216)(207,220)(208,224)
(226,229)(227,233)(228,237)(231,234)(232,238)(236,239)(241,273)(242,277)
(243,281)(244,285)(245,274)(246,278)(247,282)(248,286)(249,275)(250,279)
(251,283)(252,287)(253,276)(254,280)(255,284)(256,288)(258,261)(259,265)
(260,269)(263,266)(264,270)(268,271);;
s2 := ( 1, 49)( 2, 50)( 3, 52)( 4, 51)( 5, 61)( 6, 62)( 7, 64)( 8, 63)
( 9, 57)( 10, 58)( 11, 60)( 12, 59)( 13, 53)( 14, 54)( 15, 56)( 16, 55)
( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 93)( 22, 94)( 23, 96)( 24, 95)
( 25, 89)( 26, 90)( 27, 92)( 28, 91)( 29, 85)( 30, 86)( 31, 88)( 32, 87)
( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 77)( 38, 78)( 39, 80)( 40, 79)
( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)( 48, 71)
( 99,100)(101,109)(102,110)(103,112)(104,111)(107,108)(113,129)(114,130)
(115,132)(116,131)(117,141)(118,142)(119,144)(120,143)(121,137)(122,138)
(123,140)(124,139)(125,133)(126,134)(127,136)(128,135)(145,193)(146,194)
(147,196)(148,195)(149,205)(150,206)(151,208)(152,207)(153,201)(154,202)
(155,204)(156,203)(157,197)(158,198)(159,200)(160,199)(161,225)(162,226)
(163,228)(164,227)(165,237)(166,238)(167,240)(168,239)(169,233)(170,234)
(171,236)(172,235)(173,229)(174,230)(175,232)(176,231)(177,209)(178,210)
(179,212)(180,211)(181,221)(182,222)(183,224)(184,223)(185,217)(186,218)
(187,220)(188,219)(189,213)(190,214)(191,216)(192,215)(243,244)(245,253)
(246,254)(247,256)(248,255)(251,252)(257,273)(258,274)(259,276)(260,275)
(261,285)(262,286)(263,288)(264,287)(265,281)(266,282)(267,284)(268,283)
(269,277)(270,278)(271,280)(272,279);;
s3 := ( 1,257)( 2,260)( 3,259)( 4,258)( 5,269)( 6,272)( 7,271)( 8,270)
( 9,265)( 10,268)( 11,267)( 12,266)( 13,261)( 14,264)( 15,263)( 16,262)
( 17,241)( 18,244)( 19,243)( 20,242)( 21,253)( 22,256)( 23,255)( 24,254)
( 25,249)( 26,252)( 27,251)( 28,250)( 29,245)( 30,248)( 31,247)( 32,246)
( 33,273)( 34,276)( 35,275)( 36,274)( 37,285)( 38,288)( 39,287)( 40,286)
( 41,281)( 42,284)( 43,283)( 44,282)( 45,277)( 46,280)( 47,279)( 48,278)
( 49,209)( 50,212)( 51,211)( 52,210)( 53,221)( 54,224)( 55,223)( 56,222)
( 57,217)( 58,220)( 59,219)( 60,218)( 61,213)( 62,216)( 63,215)( 64,214)
( 65,193)( 66,196)( 67,195)( 68,194)( 69,205)( 70,208)( 71,207)( 72,206)
( 73,201)( 74,204)( 75,203)( 76,202)( 77,197)( 78,200)( 79,199)( 80,198)
( 81,225)( 82,228)( 83,227)( 84,226)( 85,237)( 86,240)( 87,239)( 88,238)
( 89,233)( 90,236)( 91,235)( 92,234)( 93,229)( 94,232)( 95,231)( 96,230)
( 97,161)( 98,164)( 99,163)(100,162)(101,173)(102,176)(103,175)(104,174)
(105,169)(106,172)(107,171)(108,170)(109,165)(110,168)(111,167)(112,166)
(113,145)(114,148)(115,147)(116,146)(117,157)(118,160)(119,159)(120,158)
(121,153)(122,156)(123,155)(124,154)(125,149)(126,152)(127,151)(128,150)
(129,177)(130,180)(131,179)(132,178)(133,189)(134,192)(135,191)(136,190)
(137,185)(138,188)(139,187)(140,186)(141,181)(142,184)(143,183)(144,182);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s3*s2*s1*s0*s1*s2*s1*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)
(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)
(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)
(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)
(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)
(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)
(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)
(280,288);
s1 := Sym(288)!( 2, 5)( 3, 9)( 4, 13)( 7, 10)( 8, 14)( 12, 15)( 17, 33)
( 18, 37)( 19, 41)( 20, 45)( 21, 34)( 22, 38)( 23, 42)( 24, 46)( 25, 35)
( 26, 39)( 27, 43)( 28, 47)( 29, 36)( 30, 40)( 31, 44)( 32, 48)( 49, 65)
( 50, 69)( 51, 73)( 52, 77)( 53, 66)( 54, 70)( 55, 74)( 56, 78)( 57, 67)
( 58, 71)( 59, 75)( 60, 79)( 61, 68)( 62, 72)( 63, 76)( 64, 80)( 82, 85)
( 83, 89)( 84, 93)( 87, 90)( 88, 94)( 92, 95)( 97,129)( 98,133)( 99,137)
(100,141)(101,130)(102,134)(103,138)(104,142)(105,131)(106,135)(107,139)
(108,143)(109,132)(110,136)(111,140)(112,144)(114,117)(115,121)(116,125)
(119,122)(120,126)(124,127)(146,149)(147,153)(148,157)(151,154)(152,158)
(156,159)(161,177)(162,181)(163,185)(164,189)(165,178)(166,182)(167,186)
(168,190)(169,179)(170,183)(171,187)(172,191)(173,180)(174,184)(175,188)
(176,192)(193,209)(194,213)(195,217)(196,221)(197,210)(198,214)(199,218)
(200,222)(201,211)(202,215)(203,219)(204,223)(205,212)(206,216)(207,220)
(208,224)(226,229)(227,233)(228,237)(231,234)(232,238)(236,239)(241,273)
(242,277)(243,281)(244,285)(245,274)(246,278)(247,282)(248,286)(249,275)
(250,279)(251,283)(252,287)(253,276)(254,280)(255,284)(256,288)(258,261)
(259,265)(260,269)(263,266)(264,270)(268,271);
s2 := Sym(288)!( 1, 49)( 2, 50)( 3, 52)( 4, 51)( 5, 61)( 6, 62)( 7, 64)
( 8, 63)( 9, 57)( 10, 58)( 11, 60)( 12, 59)( 13, 53)( 14, 54)( 15, 56)
( 16, 55)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 93)( 22, 94)( 23, 96)
( 24, 95)( 25, 89)( 26, 90)( 27, 92)( 28, 91)( 29, 85)( 30, 86)( 31, 88)
( 32, 87)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 77)( 38, 78)( 39, 80)
( 40, 79)( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)
( 48, 71)( 99,100)(101,109)(102,110)(103,112)(104,111)(107,108)(113,129)
(114,130)(115,132)(116,131)(117,141)(118,142)(119,144)(120,143)(121,137)
(122,138)(123,140)(124,139)(125,133)(126,134)(127,136)(128,135)(145,193)
(146,194)(147,196)(148,195)(149,205)(150,206)(151,208)(152,207)(153,201)
(154,202)(155,204)(156,203)(157,197)(158,198)(159,200)(160,199)(161,225)
(162,226)(163,228)(164,227)(165,237)(166,238)(167,240)(168,239)(169,233)
(170,234)(171,236)(172,235)(173,229)(174,230)(175,232)(176,231)(177,209)
(178,210)(179,212)(180,211)(181,221)(182,222)(183,224)(184,223)(185,217)
(186,218)(187,220)(188,219)(189,213)(190,214)(191,216)(192,215)(243,244)
(245,253)(246,254)(247,256)(248,255)(251,252)(257,273)(258,274)(259,276)
(260,275)(261,285)(262,286)(263,288)(264,287)(265,281)(266,282)(267,284)
(268,283)(269,277)(270,278)(271,280)(272,279);
s3 := Sym(288)!( 1,257)( 2,260)( 3,259)( 4,258)( 5,269)( 6,272)( 7,271)
( 8,270)( 9,265)( 10,268)( 11,267)( 12,266)( 13,261)( 14,264)( 15,263)
( 16,262)( 17,241)( 18,244)( 19,243)( 20,242)( 21,253)( 22,256)( 23,255)
( 24,254)( 25,249)( 26,252)( 27,251)( 28,250)( 29,245)( 30,248)( 31,247)
( 32,246)( 33,273)( 34,276)( 35,275)( 36,274)( 37,285)( 38,288)( 39,287)
( 40,286)( 41,281)( 42,284)( 43,283)( 44,282)( 45,277)( 46,280)( 47,279)
( 48,278)( 49,209)( 50,212)( 51,211)( 52,210)( 53,221)( 54,224)( 55,223)
( 56,222)( 57,217)( 58,220)( 59,219)( 60,218)( 61,213)( 62,216)( 63,215)
( 64,214)( 65,193)( 66,196)( 67,195)( 68,194)( 69,205)( 70,208)( 71,207)
( 72,206)( 73,201)( 74,204)( 75,203)( 76,202)( 77,197)( 78,200)( 79,199)
( 80,198)( 81,225)( 82,228)( 83,227)( 84,226)( 85,237)( 86,240)( 87,239)
( 88,238)( 89,233)( 90,236)( 91,235)( 92,234)( 93,229)( 94,232)( 95,231)
( 96,230)( 97,161)( 98,164)( 99,163)(100,162)(101,173)(102,176)(103,175)
(104,174)(105,169)(106,172)(107,171)(108,170)(109,165)(110,168)(111,167)
(112,166)(113,145)(114,148)(115,147)(116,146)(117,157)(118,160)(119,159)
(120,158)(121,153)(122,156)(123,155)(124,154)(125,149)(126,152)(127,151)
(128,150)(129,177)(130,180)(131,179)(132,178)(133,189)(134,192)(135,191)
(136,190)(137,185)(138,188)(139,187)(140,186)(141,181)(142,184)(143,183)
(144,182);
poly := sub<Sym(288)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s3*s2*s1*s0*s1*s2*s1*s3 >;
References : None.
to this polytope