Polytope of Type {4,6,4,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,4,3}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157851)
Rank : 5
Schlafli Type : {4,6,4,3}
Number of vertices, edges, etc : 4, 12, 24, 12, 6
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Universal
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) :
4-fold quotients : {4,6,2,3}*288c
8-fold quotients : {4,3,2,3}*144
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 := ( 1,163)( 2,164)( 3,161)( 4,162)( 5,175)( 6,176)( 7,173)( 8,174)
( 9,171)( 10,172)( 11,169)( 12,170)( 13,167)( 14,168)( 15,165)( 16,166)
( 17,147)( 18,148)( 19,145)( 20,146)( 21,159)( 22,160)( 23,157)( 24,158)
( 25,155)( 26,156)( 27,153)( 28,154)( 29,151)( 30,152)( 31,149)( 32,150)
( 33,179)( 34,180)( 35,177)( 36,178)( 37,191)( 38,192)( 39,189)( 40,190)
( 41,187)( 42,188)( 43,185)( 44,186)( 45,183)( 46,184)( 47,181)( 48,182)
( 49,211)( 50,212)( 51,209)( 52,210)( 53,223)( 54,224)( 55,221)( 56,222)
( 57,219)( 58,220)( 59,217)( 60,218)( 61,215)( 62,216)( 63,213)( 64,214)
( 65,195)( 66,196)( 67,193)( 68,194)( 69,207)( 70,208)( 71,205)( 72,206)
( 73,203)( 74,204)( 75,201)( 76,202)( 77,199)( 78,200)( 79,197)( 80,198)
( 81,227)( 82,228)( 83,225)( 84,226)( 85,239)( 86,240)( 87,237)( 88,238)
( 89,235)( 90,236)( 91,233)( 92,234)( 93,231)( 94,232)( 95,229)( 96,230)
( 97,259)( 98,260)( 99,257)(100,258)(101,271)(102,272)(103,269)(104,270)
(105,267)(106,268)(107,265)(108,266)(109,263)(110,264)(111,261)(112,262)
(113,243)(114,244)(115,241)(116,242)(117,255)(118,256)(119,253)(120,254)
(121,251)(122,252)(123,249)(124,250)(125,247)(126,248)(127,245)(128,246)
(129,275)(130,276)(131,273)(132,274)(133,287)(134,288)(135,285)(136,286)
(137,283)(138,284)(139,281)(140,282)(141,279)(142,280)(143,277)(144,278);;
s3 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)
( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 49, 97)( 50, 98)( 51,100)( 52, 99)
( 53,101)( 54,102)( 55,104)( 56,103)( 57,105)( 58,106)( 59,108)( 60,107)
( 61,109)( 62,110)( 63,112)( 64,111)( 65,113)( 66,114)( 67,116)( 68,115)
( 69,117)( 70,118)( 71,120)( 72,119)( 73,121)( 74,122)( 75,124)( 76,123)
( 77,125)( 78,126)( 79,128)( 80,127)( 81,129)( 82,130)( 83,132)( 84,131)
( 85,133)( 86,134)( 87,136)( 88,135)( 89,137)( 90,138)( 91,140)( 92,139)
( 93,141)( 94,142)( 95,144)( 96,143)(147,148)(151,152)(155,156)(159,160)
(163,164)(167,168)(171,172)(175,176)(179,180)(183,184)(187,188)(191,192)
(193,241)(194,242)(195,244)(196,243)(197,245)(198,246)(199,248)(200,247)
(201,249)(202,250)(203,252)(204,251)(205,253)(206,254)(207,256)(208,255)
(209,257)(210,258)(211,260)(212,259)(213,261)(214,262)(215,264)(216,263)
(217,265)(218,266)(219,268)(220,267)(221,269)(222,270)(223,272)(224,271)
(225,273)(226,274)(227,276)(228,275)(229,277)(230,278)(231,280)(232,279)
(233,281)(234,282)(235,284)(236,283)(237,285)(238,286)(239,288)(240,287);;
s4 := ( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 53)( 6, 56)( 7, 55)( 8, 54)
( 9, 57)( 10, 60)( 11, 59)( 12, 58)( 13, 61)( 14, 64)( 15, 63)( 16, 62)
( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21, 69)( 22, 72)( 23, 71)( 24, 70)
( 25, 73)( 26, 76)( 27, 75)( 28, 74)( 29, 77)( 30, 80)( 31, 79)( 32, 78)
( 33, 81)( 34, 84)( 35, 83)( 36, 82)( 37, 85)( 38, 88)( 39, 87)( 40, 86)
( 41, 89)( 42, 92)( 43, 91)( 44, 90)( 45, 93)( 46, 96)( 47, 95)( 48, 94)
( 98,100)(102,104)(106,108)(110,112)(114,116)(118,120)(122,124)(126,128)
(130,132)(134,136)(138,140)(142,144)(145,193)(146,196)(147,195)(148,194)
(149,197)(150,200)(151,199)(152,198)(153,201)(154,204)(155,203)(156,202)
(157,205)(158,208)(159,207)(160,206)(161,209)(162,212)(163,211)(164,210)
(165,213)(166,216)(167,215)(168,214)(169,217)(170,220)(171,219)(172,218)
(173,221)(174,224)(175,223)(176,222)(177,225)(178,228)(179,227)(180,226)
(181,229)(182,232)(183,231)(184,230)(185,233)(186,236)(187,235)(188,234)
(189,237)(190,240)(191,239)(192,238)(242,244)(246,248)(250,252)(254,256)
(258,260)(262,264)(266,268)(270,272)(274,276)(278,280)(282,284)(286,288);;
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, s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)!( 1,163)( 2,164)( 3,161)( 4,162)( 5,175)( 6,176)( 7,173)
( 8,174)( 9,171)( 10,172)( 11,169)( 12,170)( 13,167)( 14,168)( 15,165)
( 16,166)( 17,147)( 18,148)( 19,145)( 20,146)( 21,159)( 22,160)( 23,157)
( 24,158)( 25,155)( 26,156)( 27,153)( 28,154)( 29,151)( 30,152)( 31,149)
( 32,150)( 33,179)( 34,180)( 35,177)( 36,178)( 37,191)( 38,192)( 39,189)
( 40,190)( 41,187)( 42,188)( 43,185)( 44,186)( 45,183)( 46,184)( 47,181)
( 48,182)( 49,211)( 50,212)( 51,209)( 52,210)( 53,223)( 54,224)( 55,221)
( 56,222)( 57,219)( 58,220)( 59,217)( 60,218)( 61,215)( 62,216)( 63,213)
( 64,214)( 65,195)( 66,196)( 67,193)( 68,194)( 69,207)( 70,208)( 71,205)
( 72,206)( 73,203)( 74,204)( 75,201)( 76,202)( 77,199)( 78,200)( 79,197)
( 80,198)( 81,227)( 82,228)( 83,225)( 84,226)( 85,239)( 86,240)( 87,237)
( 88,238)( 89,235)( 90,236)( 91,233)( 92,234)( 93,231)( 94,232)( 95,229)
( 96,230)( 97,259)( 98,260)( 99,257)(100,258)(101,271)(102,272)(103,269)
(104,270)(105,267)(106,268)(107,265)(108,266)(109,263)(110,264)(111,261)
(112,262)(113,243)(114,244)(115,241)(116,242)(117,255)(118,256)(119,253)
(120,254)(121,251)(122,252)(123,249)(124,250)(125,247)(126,248)(127,245)
(128,246)(129,275)(130,276)(131,273)(132,274)(133,287)(134,288)(135,285)
(136,286)(137,283)(138,284)(139,281)(140,282)(141,279)(142,280)(143,277)
(144,278);
s3 := Sym(288)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)
( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 49, 97)( 50, 98)( 51,100)
( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,105)( 58,106)( 59,108)
( 60,107)( 61,109)( 62,110)( 63,112)( 64,111)( 65,113)( 66,114)( 67,116)
( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,121)( 74,122)( 75,124)
( 76,123)( 77,125)( 78,126)( 79,128)( 80,127)( 81,129)( 82,130)( 83,132)
( 84,131)( 85,133)( 86,134)( 87,136)( 88,135)( 89,137)( 90,138)( 91,140)
( 92,139)( 93,141)( 94,142)( 95,144)( 96,143)(147,148)(151,152)(155,156)
(159,160)(163,164)(167,168)(171,172)(175,176)(179,180)(183,184)(187,188)
(191,192)(193,241)(194,242)(195,244)(196,243)(197,245)(198,246)(199,248)
(200,247)(201,249)(202,250)(203,252)(204,251)(205,253)(206,254)(207,256)
(208,255)(209,257)(210,258)(211,260)(212,259)(213,261)(214,262)(215,264)
(216,263)(217,265)(218,266)(219,268)(220,267)(221,269)(222,270)(223,272)
(224,271)(225,273)(226,274)(227,276)(228,275)(229,277)(230,278)(231,280)
(232,279)(233,281)(234,282)(235,284)(236,283)(237,285)(238,286)(239,288)
(240,287);
s4 := Sym(288)!( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 53)( 6, 56)( 7, 55)
( 8, 54)( 9, 57)( 10, 60)( 11, 59)( 12, 58)( 13, 61)( 14, 64)( 15, 63)
( 16, 62)( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21, 69)( 22, 72)( 23, 71)
( 24, 70)( 25, 73)( 26, 76)( 27, 75)( 28, 74)( 29, 77)( 30, 80)( 31, 79)
( 32, 78)( 33, 81)( 34, 84)( 35, 83)( 36, 82)( 37, 85)( 38, 88)( 39, 87)
( 40, 86)( 41, 89)( 42, 92)( 43, 91)( 44, 90)( 45, 93)( 46, 96)( 47, 95)
( 48, 94)( 98,100)(102,104)(106,108)(110,112)(114,116)(118,120)(122,124)
(126,128)(130,132)(134,136)(138,140)(142,144)(145,193)(146,196)(147,195)
(148,194)(149,197)(150,200)(151,199)(152,198)(153,201)(154,204)(155,203)
(156,202)(157,205)(158,208)(159,207)(160,206)(161,209)(162,212)(163,211)
(164,210)(165,213)(166,216)(167,215)(168,214)(169,217)(170,220)(171,219)
(172,218)(173,221)(174,224)(175,223)(176,222)(177,225)(178,228)(179,227)
(180,226)(181,229)(182,232)(183,231)(184,230)(185,233)(186,236)(187,235)
(188,234)(189,237)(190,240)(191,239)(192,238)(242,244)(246,248)(250,252)
(254,256)(258,260)(262,264)(266,268)(270,272)(274,276)(278,280)(282,284)
(286,288);
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, s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope