Polytope of Type {6,6,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,8}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 4
Schlafli Type : {6,6,8}
Number of vertices, edges, etc : 6, 36, 48, 16
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {6,6,4}*576a
3-fold quotients : {2,6,8}*384b
4-fold quotients : {6,6,4}*288d
6-fold quotients : {2,3,8}*192, {2,6,4}*192
8-fold quotients : {6,6,2}*144a
12-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
24-fold quotients : {2,3,4}*48, {2,6,2}*48, {6,2,2}*48
48-fold quotients : {2,3,2}*24, {3,2,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(153,161)(154,162)(155,163)(156,164)(157,165)(158,166)(159,167)(160,168)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(249,257)(250,258)(251,259)(252,260)(253,261)(254,262)(255,263)(256,264)
(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288);;
s1 := ( 1, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 15)( 6, 16)( 7, 13)( 8, 14)
( 19, 20)( 21, 23)( 22, 24)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 63)
( 30, 64)( 31, 61)( 32, 62)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 55)
( 38, 56)( 39, 53)( 40, 54)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)
( 46, 72)( 47, 69)( 48, 70)( 73, 82)( 74, 81)( 75, 83)( 76, 84)( 77, 88)
( 78, 87)( 79, 86)( 80, 85)( 89, 90)( 93, 96)( 94, 95)( 97,130)( 98,129)
( 99,131)(100,132)(101,136)(102,135)(103,134)(104,133)(105,122)(106,121)
(107,123)(108,124)(109,128)(110,127)(111,126)(112,125)(113,138)(114,137)
(115,139)(116,140)(117,144)(118,143)(119,142)(120,141)(145,153)(146,154)
(147,156)(148,155)(149,159)(150,160)(151,157)(152,158)(163,164)(165,167)
(166,168)(169,201)(170,202)(171,204)(172,203)(173,207)(174,208)(175,205)
(176,206)(177,193)(178,194)(179,196)(180,195)(181,199)(182,200)(183,197)
(184,198)(185,209)(186,210)(187,212)(188,211)(189,215)(190,216)(191,213)
(192,214)(217,226)(218,225)(219,227)(220,228)(221,232)(222,231)(223,230)
(224,229)(233,234)(237,240)(238,239)(241,274)(242,273)(243,275)(244,276)
(245,280)(246,279)(247,278)(248,277)(249,266)(250,265)(251,267)(252,268)
(253,272)(254,271)(255,270)(256,269)(257,282)(258,281)(259,283)(260,284)
(261,288)(262,287)(263,286)(264,285);;
s2 := ( 1,169)( 2,170)( 3,175)( 4,176)( 5,174)( 6,173)( 7,171)( 8,172)
( 9,177)( 10,178)( 11,183)( 12,184)( 13,182)( 14,181)( 15,179)( 16,180)
( 17,185)( 18,186)( 19,191)( 20,192)( 21,190)( 22,189)( 23,187)( 24,188)
( 25,145)( 26,146)( 27,151)( 28,152)( 29,150)( 30,149)( 31,147)( 32,148)
( 33,153)( 34,154)( 35,159)( 36,160)( 37,158)( 38,157)( 39,155)( 40,156)
( 41,161)( 42,162)( 43,167)( 44,168)( 45,166)( 46,165)( 47,163)( 48,164)
( 49,193)( 50,194)( 51,199)( 52,200)( 53,198)( 54,197)( 55,195)( 56,196)
( 57,201)( 58,202)( 59,207)( 60,208)( 61,206)( 62,205)( 63,203)( 64,204)
( 65,209)( 66,210)( 67,215)( 68,216)( 69,214)( 70,213)( 71,211)( 72,212)
( 73,242)( 74,241)( 75,248)( 76,247)( 77,245)( 78,246)( 79,244)( 80,243)
( 81,250)( 82,249)( 83,256)( 84,255)( 85,253)( 86,254)( 87,252)( 88,251)
( 89,258)( 90,257)( 91,264)( 92,263)( 93,261)( 94,262)( 95,260)( 96,259)
( 97,218)( 98,217)( 99,224)(100,223)(101,221)(102,222)(103,220)(104,219)
(105,226)(106,225)(107,232)(108,231)(109,229)(110,230)(111,228)(112,227)
(113,234)(114,233)(115,240)(116,239)(117,237)(118,238)(119,236)(120,235)
(121,266)(122,265)(123,272)(124,271)(125,269)(126,270)(127,268)(128,267)
(129,274)(130,273)(131,280)(132,279)(133,277)(134,278)(135,276)(136,275)
(137,282)(138,281)(139,288)(140,287)(141,285)(142,286)(143,284)(144,283);;
s3 := ( 1, 75)( 2, 76)( 3, 74)( 4, 73)( 5, 79)( 6, 80)( 7, 78)( 8, 77)
( 9, 83)( 10, 84)( 11, 82)( 12, 81)( 13, 87)( 14, 88)( 15, 86)( 16, 85)
( 17, 91)( 18, 92)( 19, 90)( 20, 89)( 21, 95)( 22, 96)( 23, 94)( 24, 93)
( 25, 99)( 26,100)( 27, 98)( 28, 97)( 29,103)( 30,104)( 31,102)( 32,101)
( 33,107)( 34,108)( 35,106)( 36,105)( 37,111)( 38,112)( 39,110)( 40,109)
( 41,115)( 42,116)( 43,114)( 44,113)( 45,119)( 46,120)( 47,118)( 48,117)
( 49,123)( 50,124)( 51,122)( 52,121)( 53,127)( 54,128)( 55,126)( 56,125)
( 57,131)( 58,132)( 59,130)( 60,129)( 61,135)( 62,136)( 63,134)( 64,133)
( 65,139)( 66,140)( 67,138)( 68,137)( 69,143)( 70,144)( 71,142)( 72,141)
(145,219)(146,220)(147,218)(148,217)(149,223)(150,224)(151,222)(152,221)
(153,227)(154,228)(155,226)(156,225)(157,231)(158,232)(159,230)(160,229)
(161,235)(162,236)(163,234)(164,233)(165,239)(166,240)(167,238)(168,237)
(169,243)(170,244)(171,242)(172,241)(173,247)(174,248)(175,246)(176,245)
(177,251)(178,252)(179,250)(180,249)(181,255)(182,256)(183,254)(184,253)
(185,259)(186,260)(187,258)(188,257)(189,263)(190,264)(191,262)(192,261)
(193,267)(194,268)(195,266)(196,265)(197,271)(198,272)(199,270)(200,269)
(201,275)(202,276)(203,274)(204,273)(205,279)(206,280)(207,278)(208,277)
(209,283)(210,284)(211,282)(212,281)(213,287)(214,288)(215,286)(216,285);;
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*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)
( 16, 24)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)
( 64, 72)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)
(112,120)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(153,161)(154,162)(155,163)(156,164)(157,165)(158,166)(159,167)
(160,168)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)
(208,216)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(249,257)(250,258)(251,259)(252,260)(253,261)(254,262)(255,263)
(256,264)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)
(280,288);
s1 := Sym(288)!( 1, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 15)( 6, 16)( 7, 13)
( 8, 14)( 19, 20)( 21, 23)( 22, 24)( 25, 57)( 26, 58)( 27, 60)( 28, 59)
( 29, 63)( 30, 64)( 31, 61)( 32, 62)( 33, 49)( 34, 50)( 35, 52)( 36, 51)
( 37, 55)( 38, 56)( 39, 53)( 40, 54)( 41, 65)( 42, 66)( 43, 68)( 44, 67)
( 45, 71)( 46, 72)( 47, 69)( 48, 70)( 73, 82)( 74, 81)( 75, 83)( 76, 84)
( 77, 88)( 78, 87)( 79, 86)( 80, 85)( 89, 90)( 93, 96)( 94, 95)( 97,130)
( 98,129)( 99,131)(100,132)(101,136)(102,135)(103,134)(104,133)(105,122)
(106,121)(107,123)(108,124)(109,128)(110,127)(111,126)(112,125)(113,138)
(114,137)(115,139)(116,140)(117,144)(118,143)(119,142)(120,141)(145,153)
(146,154)(147,156)(148,155)(149,159)(150,160)(151,157)(152,158)(163,164)
(165,167)(166,168)(169,201)(170,202)(171,204)(172,203)(173,207)(174,208)
(175,205)(176,206)(177,193)(178,194)(179,196)(180,195)(181,199)(182,200)
(183,197)(184,198)(185,209)(186,210)(187,212)(188,211)(189,215)(190,216)
(191,213)(192,214)(217,226)(218,225)(219,227)(220,228)(221,232)(222,231)
(223,230)(224,229)(233,234)(237,240)(238,239)(241,274)(242,273)(243,275)
(244,276)(245,280)(246,279)(247,278)(248,277)(249,266)(250,265)(251,267)
(252,268)(253,272)(254,271)(255,270)(256,269)(257,282)(258,281)(259,283)
(260,284)(261,288)(262,287)(263,286)(264,285);
s2 := Sym(288)!( 1,169)( 2,170)( 3,175)( 4,176)( 5,174)( 6,173)( 7,171)
( 8,172)( 9,177)( 10,178)( 11,183)( 12,184)( 13,182)( 14,181)( 15,179)
( 16,180)( 17,185)( 18,186)( 19,191)( 20,192)( 21,190)( 22,189)( 23,187)
( 24,188)( 25,145)( 26,146)( 27,151)( 28,152)( 29,150)( 30,149)( 31,147)
( 32,148)( 33,153)( 34,154)( 35,159)( 36,160)( 37,158)( 38,157)( 39,155)
( 40,156)( 41,161)( 42,162)( 43,167)( 44,168)( 45,166)( 46,165)( 47,163)
( 48,164)( 49,193)( 50,194)( 51,199)( 52,200)( 53,198)( 54,197)( 55,195)
( 56,196)( 57,201)( 58,202)( 59,207)( 60,208)( 61,206)( 62,205)( 63,203)
( 64,204)( 65,209)( 66,210)( 67,215)( 68,216)( 69,214)( 70,213)( 71,211)
( 72,212)( 73,242)( 74,241)( 75,248)( 76,247)( 77,245)( 78,246)( 79,244)
( 80,243)( 81,250)( 82,249)( 83,256)( 84,255)( 85,253)( 86,254)( 87,252)
( 88,251)( 89,258)( 90,257)( 91,264)( 92,263)( 93,261)( 94,262)( 95,260)
( 96,259)( 97,218)( 98,217)( 99,224)(100,223)(101,221)(102,222)(103,220)
(104,219)(105,226)(106,225)(107,232)(108,231)(109,229)(110,230)(111,228)
(112,227)(113,234)(114,233)(115,240)(116,239)(117,237)(118,238)(119,236)
(120,235)(121,266)(122,265)(123,272)(124,271)(125,269)(126,270)(127,268)
(128,267)(129,274)(130,273)(131,280)(132,279)(133,277)(134,278)(135,276)
(136,275)(137,282)(138,281)(139,288)(140,287)(141,285)(142,286)(143,284)
(144,283);
s3 := Sym(288)!( 1, 75)( 2, 76)( 3, 74)( 4, 73)( 5, 79)( 6, 80)( 7, 78)
( 8, 77)( 9, 83)( 10, 84)( 11, 82)( 12, 81)( 13, 87)( 14, 88)( 15, 86)
( 16, 85)( 17, 91)( 18, 92)( 19, 90)( 20, 89)( 21, 95)( 22, 96)( 23, 94)
( 24, 93)( 25, 99)( 26,100)( 27, 98)( 28, 97)( 29,103)( 30,104)( 31,102)
( 32,101)( 33,107)( 34,108)( 35,106)( 36,105)( 37,111)( 38,112)( 39,110)
( 40,109)( 41,115)( 42,116)( 43,114)( 44,113)( 45,119)( 46,120)( 47,118)
( 48,117)( 49,123)( 50,124)( 51,122)( 52,121)( 53,127)( 54,128)( 55,126)
( 56,125)( 57,131)( 58,132)( 59,130)( 60,129)( 61,135)( 62,136)( 63,134)
( 64,133)( 65,139)( 66,140)( 67,138)( 68,137)( 69,143)( 70,144)( 71,142)
( 72,141)(145,219)(146,220)(147,218)(148,217)(149,223)(150,224)(151,222)
(152,221)(153,227)(154,228)(155,226)(156,225)(157,231)(158,232)(159,230)
(160,229)(161,235)(162,236)(163,234)(164,233)(165,239)(166,240)(167,238)
(168,237)(169,243)(170,244)(171,242)(172,241)(173,247)(174,248)(175,246)
(176,245)(177,251)(178,252)(179,250)(180,249)(181,255)(182,256)(183,254)
(184,253)(185,259)(186,260)(187,258)(188,257)(189,263)(190,264)(191,262)
(192,261)(193,267)(194,268)(195,266)(196,265)(197,271)(198,272)(199,270)
(200,269)(201,275)(202,276)(203,274)(204,273)(205,279)(206,280)(207,278)
(208,277)(209,283)(210,284)(211,282)(212,281)(213,287)(214,288)(215,286)
(216,285);
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*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2 >;
References : None.
to this polytope