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