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