Polytope of Type {4,6,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,6,4}*1152j
if this polytope has a name.
Group : SmallGroup(1152,157851)
Rank : 5
Schlafli Type : {4,6,6,4}
Number of vertices, edges, etc : 4, 12, 18, 12, 4
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
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 := ( 9, 13)( 10, 14)( 11, 15)( 12, 16)( 17, 33)( 18, 34)( 19, 35)( 20, 36)
( 21, 37)( 22, 38)( 23, 39)( 24, 40)( 25, 45)( 26, 46)( 27, 47)( 28, 48)
( 29, 41)( 30, 42)( 31, 43)( 32, 44)( 57, 61)( 58, 62)( 59, 63)( 60, 64)
( 65, 81)( 66, 82)( 67, 83)( 68, 84)( 69, 85)( 70, 86)( 71, 87)( 72, 88)
( 73, 93)( 74, 94)( 75, 95)( 76, 96)( 77, 89)( 78, 90)( 79, 91)( 80, 92)
(105,109)(106,110)(107,111)(108,112)(113,129)(114,130)(115,131)(116,132)
(117,133)(118,134)(119,135)(120,136)(121,141)(122,142)(123,143)(124,144)
(125,137)(126,138)(127,139)(128,140)(153,157)(154,158)(155,159)(156,160)
(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,183)(168,184)
(169,189)(170,190)(171,191)(172,192)(173,185)(174,186)(175,187)(176,188)
(201,205)(202,206)(203,207)(204,208)(209,225)(210,226)(211,227)(212,228)
(213,229)(214,230)(215,231)(216,232)(217,237)(218,238)(219,239)(220,240)
(221,233)(222,234)(223,235)(224,236)(249,253)(250,254)(251,255)(252,256)
(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)(264,280)
(265,285)(266,286)(267,287)(268,288)(269,281)(270,282)(271,283)(272,284);;
s2 := ( 1, 17)( 2, 18)( 3, 20)( 4, 19)( 5, 29)( 6, 30)( 7, 32)( 8, 31)
( 9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 21)( 14, 22)( 15, 24)( 16, 23)
( 35, 36)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 43, 44)( 49,113)( 50,114)
( 51,116)( 52,115)( 53,125)( 54,126)( 55,128)( 56,127)( 57,121)( 58,122)
( 59,124)( 60,123)( 61,117)( 62,118)( 63,120)( 64,119)( 65, 97)( 66, 98)
( 67,100)( 68, 99)( 69,109)( 70,110)( 71,112)( 72,111)( 73,105)( 74,106)
( 75,108)( 76,107)( 77,101)( 78,102)( 79,104)( 80,103)( 81,129)( 82,130)
( 83,132)( 84,131)( 85,141)( 86,142)( 87,144)( 88,143)( 89,137)( 90,138)
( 91,140)( 92,139)( 93,133)( 94,134)( 95,136)( 96,135)(145,161)(146,162)
(147,164)(148,163)(149,173)(150,174)(151,176)(152,175)(153,169)(154,170)
(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(179,180)(181,189)
(182,190)(183,192)(184,191)(187,188)(193,257)(194,258)(195,260)(196,259)
(197,269)(198,270)(199,272)(200,271)(201,265)(202,266)(203,268)(204,267)
(205,261)(206,262)(207,264)(208,263)(209,241)(210,242)(211,244)(212,243)
(213,253)(214,254)(215,256)(216,255)(217,249)(218,250)(219,252)(220,251)
(221,245)(222,246)(223,248)(224,247)(225,273)(226,274)(227,276)(228,275)
(229,285)(230,286)(231,288)(232,287)(233,281)(234,282)(235,284)(236,283)
(237,277)(238,278)(239,280)(240,279);;
s3 := ( 1,193)( 2,196)( 3,195)( 4,194)( 5,197)( 6,200)( 7,199)( 8,198)
( 9,201)( 10,204)( 11,203)( 12,202)( 13,205)( 14,208)( 15,207)( 16,206)
( 17,209)( 18,212)( 19,211)( 20,210)( 21,213)( 22,216)( 23,215)( 24,214)
( 25,217)( 26,220)( 27,219)( 28,218)( 29,221)( 30,224)( 31,223)( 32,222)
( 33,225)( 34,228)( 35,227)( 36,226)( 37,229)( 38,232)( 39,231)( 40,230)
( 41,233)( 42,236)( 43,235)( 44,234)( 45,237)( 46,240)( 47,239)( 48,238)
( 49,145)( 50,148)( 51,147)( 52,146)( 53,149)( 54,152)( 55,151)( 56,150)
( 57,153)( 58,156)( 59,155)( 60,154)( 61,157)( 62,160)( 63,159)( 64,158)
( 65,161)( 66,164)( 67,163)( 68,162)( 69,165)( 70,168)( 71,167)( 72,166)
( 73,169)( 74,172)( 75,171)( 76,170)( 77,173)( 78,176)( 79,175)( 80,174)
( 81,177)( 82,180)( 83,179)( 84,178)( 85,181)( 86,184)( 87,183)( 88,182)
( 89,185)( 90,188)( 91,187)( 92,186)( 93,189)( 94,192)( 95,191)( 96,190)
( 97,241)( 98,244)( 99,243)(100,242)(101,245)(102,248)(103,247)(104,246)
(105,249)(106,252)(107,251)(108,250)(109,253)(110,256)(111,255)(112,254)
(113,257)(114,260)(115,259)(116,258)(117,261)(118,264)(119,263)(120,262)
(121,265)(122,268)(123,267)(124,266)(125,269)(126,272)(127,271)(128,270)
(129,273)(130,276)(131,275)(132,274)(133,277)(134,280)(135,279)(136,278)
(137,281)(138,284)(139,283)(140,282)(141,285)(142,288)(143,287)(144,286);;
s4 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s4*s3*s2*s4*s3*s4*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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)!( 9, 13)( 10, 14)( 11, 15)( 12, 16)( 17, 33)( 18, 34)( 19, 35)
( 20, 36)( 21, 37)( 22, 38)( 23, 39)( 24, 40)( 25, 45)( 26, 46)( 27, 47)
( 28, 48)( 29, 41)( 30, 42)( 31, 43)( 32, 44)( 57, 61)( 58, 62)( 59, 63)
( 60, 64)( 65, 81)( 66, 82)( 67, 83)( 68, 84)( 69, 85)( 70, 86)( 71, 87)
( 72, 88)( 73, 93)( 74, 94)( 75, 95)( 76, 96)( 77, 89)( 78, 90)( 79, 91)
( 80, 92)(105,109)(106,110)(107,111)(108,112)(113,129)(114,130)(115,131)
(116,132)(117,133)(118,134)(119,135)(120,136)(121,141)(122,142)(123,143)
(124,144)(125,137)(126,138)(127,139)(128,140)(153,157)(154,158)(155,159)
(156,160)(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,183)
(168,184)(169,189)(170,190)(171,191)(172,192)(173,185)(174,186)(175,187)
(176,188)(201,205)(202,206)(203,207)(204,208)(209,225)(210,226)(211,227)
(212,228)(213,229)(214,230)(215,231)(216,232)(217,237)(218,238)(219,239)
(220,240)(221,233)(222,234)(223,235)(224,236)(249,253)(250,254)(251,255)
(252,256)(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)
(264,280)(265,285)(266,286)(267,287)(268,288)(269,281)(270,282)(271,283)
(272,284);
s2 := Sym(288)!( 1, 17)( 2, 18)( 3, 20)( 4, 19)( 5, 29)( 6, 30)( 7, 32)
( 8, 31)( 9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 21)( 14, 22)( 15, 24)
( 16, 23)( 35, 36)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 43, 44)( 49,113)
( 50,114)( 51,116)( 52,115)( 53,125)( 54,126)( 55,128)( 56,127)( 57,121)
( 58,122)( 59,124)( 60,123)( 61,117)( 62,118)( 63,120)( 64,119)( 65, 97)
( 66, 98)( 67,100)( 68, 99)( 69,109)( 70,110)( 71,112)( 72,111)( 73,105)
( 74,106)( 75,108)( 76,107)( 77,101)( 78,102)( 79,104)( 80,103)( 81,129)
( 82,130)( 83,132)( 84,131)( 85,141)( 86,142)( 87,144)( 88,143)( 89,137)
( 90,138)( 91,140)( 92,139)( 93,133)( 94,134)( 95,136)( 96,135)(145,161)
(146,162)(147,164)(148,163)(149,173)(150,174)(151,176)(152,175)(153,169)
(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(179,180)
(181,189)(182,190)(183,192)(184,191)(187,188)(193,257)(194,258)(195,260)
(196,259)(197,269)(198,270)(199,272)(200,271)(201,265)(202,266)(203,268)
(204,267)(205,261)(206,262)(207,264)(208,263)(209,241)(210,242)(211,244)
(212,243)(213,253)(214,254)(215,256)(216,255)(217,249)(218,250)(219,252)
(220,251)(221,245)(222,246)(223,248)(224,247)(225,273)(226,274)(227,276)
(228,275)(229,285)(230,286)(231,288)(232,287)(233,281)(234,282)(235,284)
(236,283)(237,277)(238,278)(239,280)(240,279);
s3 := Sym(288)!( 1,193)( 2,196)( 3,195)( 4,194)( 5,197)( 6,200)( 7,199)
( 8,198)( 9,201)( 10,204)( 11,203)( 12,202)( 13,205)( 14,208)( 15,207)
( 16,206)( 17,209)( 18,212)( 19,211)( 20,210)( 21,213)( 22,216)( 23,215)
( 24,214)( 25,217)( 26,220)( 27,219)( 28,218)( 29,221)( 30,224)( 31,223)
( 32,222)( 33,225)( 34,228)( 35,227)( 36,226)( 37,229)( 38,232)( 39,231)
( 40,230)( 41,233)( 42,236)( 43,235)( 44,234)( 45,237)( 46,240)( 47,239)
( 48,238)( 49,145)( 50,148)( 51,147)( 52,146)( 53,149)( 54,152)( 55,151)
( 56,150)( 57,153)( 58,156)( 59,155)( 60,154)( 61,157)( 62,160)( 63,159)
( 64,158)( 65,161)( 66,164)( 67,163)( 68,162)( 69,165)( 70,168)( 71,167)
( 72,166)( 73,169)( 74,172)( 75,171)( 76,170)( 77,173)( 78,176)( 79,175)
( 80,174)( 81,177)( 82,180)( 83,179)( 84,178)( 85,181)( 86,184)( 87,183)
( 88,182)( 89,185)( 90,188)( 91,187)( 92,186)( 93,189)( 94,192)( 95,191)
( 96,190)( 97,241)( 98,244)( 99,243)(100,242)(101,245)(102,248)(103,247)
(104,246)(105,249)(106,252)(107,251)(108,250)(109,253)(110,256)(111,255)
(112,254)(113,257)(114,260)(115,259)(116,258)(117,261)(118,264)(119,263)
(120,262)(121,265)(122,268)(123,267)(124,266)(125,269)(126,272)(127,271)
(128,270)(129,273)(130,276)(131,275)(132,274)(133,277)(134,280)(135,279)
(136,278)(137,281)(138,284)(139,283)(140,282)(141,285)(142,288)(143,287)
(144,286);
s4 := Sym(288)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288);
poly := sub<Sym(288)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s4*s3*s2*s4*s3*s4*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope