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