Polytope of Type {6,12,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,6}*1152f
if this polytope has a name.
Group : SmallGroup(1152,157851)
Rank : 4
Schlafli Type : {6,12,6}
Number of vertices, edges, etc : 8, 48, 48, 6
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 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) :
12-fold quotients : {2,4,6}*96b
24-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 1,201)( 2,204)( 3,203)( 4,202)( 5,205)( 6,208)( 7,207)( 8,206)
( 9,193)( 10,196)( 11,195)( 12,194)( 13,197)( 14,200)( 15,199)( 16,198)
( 17,217)( 18,220)( 19,219)( 20,218)( 21,221)( 22,224)( 23,223)( 24,222)
( 25,209)( 26,212)( 27,211)( 28,210)( 29,213)( 30,216)( 31,215)( 32,214)
( 33,233)( 34,236)( 35,235)( 36,234)( 37,237)( 38,240)( 39,239)( 40,238)
( 41,225)( 42,228)( 43,227)( 44,226)( 45,229)( 46,232)( 47,231)( 48,230)
( 49,153)( 50,156)( 51,155)( 52,154)( 53,157)( 54,160)( 55,159)( 56,158)
( 57,145)( 58,148)( 59,147)( 60,146)( 61,149)( 62,152)( 63,151)( 64,150)
( 65,169)( 66,172)( 67,171)( 68,170)( 69,173)( 70,176)( 71,175)( 72,174)
( 73,161)( 74,164)( 75,163)( 76,162)( 77,165)( 78,168)( 79,167)( 80,166)
( 81,185)( 82,188)( 83,187)( 84,186)( 85,189)( 86,192)( 87,191)( 88,190)
( 89,177)( 90,180)( 91,179)( 92,178)( 93,181)( 94,184)( 95,183)( 96,182)
( 97,249)( 98,252)( 99,251)(100,250)(101,253)(102,256)(103,255)(104,254)
(105,241)(106,244)(107,243)(108,242)(109,245)(110,248)(111,247)(112,246)
(113,265)(114,268)(115,267)(116,266)(117,269)(118,272)(119,271)(120,270)
(121,257)(122,260)(123,259)(124,258)(125,261)(126,264)(127,263)(128,262)
(129,281)(130,284)(131,283)(132,282)(133,285)(134,288)(135,287)(136,286)
(137,273)(138,276)(139,275)(140,274)(141,277)(142,280)(143,279)(144,278);;
s2 := ( 1, 2)( 5, 6)( 9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 34)( 18, 33)
( 19, 35)( 20, 36)( 21, 38)( 22, 37)( 23, 39)( 24, 40)( 25, 46)( 26, 45)
( 27, 47)( 28, 48)( 29, 42)( 30, 41)( 31, 43)( 32, 44)( 49, 98)( 50, 97)
( 51, 99)( 52,100)( 53,102)( 54,101)( 55,103)( 56,104)( 57,110)( 58,109)
( 59,111)( 60,112)( 61,106)( 62,105)( 63,107)( 64,108)( 65,130)( 66,129)
( 67,131)( 68,132)( 69,134)( 70,133)( 71,135)( 72,136)( 73,142)( 74,141)
( 75,143)( 76,144)( 77,138)( 78,137)( 79,139)( 80,140)( 81,114)( 82,113)
( 83,115)( 84,116)( 85,118)( 86,117)( 87,119)( 88,120)( 89,126)( 90,125)
( 91,127)( 92,128)( 93,122)( 94,121)( 95,123)( 96,124)(145,146)(149,150)
(153,158)(154,157)(155,159)(156,160)(161,178)(162,177)(163,179)(164,180)
(165,182)(166,181)(167,183)(168,184)(169,190)(170,189)(171,191)(172,192)
(173,186)(174,185)(175,187)(176,188)(193,242)(194,241)(195,243)(196,244)
(197,246)(198,245)(199,247)(200,248)(201,254)(202,253)(203,255)(204,256)
(205,250)(206,249)(207,251)(208,252)(209,274)(210,273)(211,275)(212,276)
(213,278)(214,277)(215,279)(216,280)(217,286)(218,285)(219,287)(220,288)
(221,282)(222,281)(223,283)(224,284)(225,258)(226,257)(227,259)(228,260)
(229,262)(230,261)(231,263)(232,264)(233,270)(234,269)(235,271)(236,272)
(237,266)(238,265)(239,267)(240,268);;
s3 := ( 1,161)( 2,162)( 3,163)( 4,164)( 5,173)( 6,174)( 7,175)( 8,176)
( 9,169)( 10,170)( 11,171)( 12,172)( 13,165)( 14,166)( 15,167)( 16,168)
( 17,145)( 18,146)( 19,147)( 20,148)( 21,157)( 22,158)( 23,159)( 24,160)
( 25,153)( 26,154)( 27,155)( 28,156)( 29,149)( 30,150)( 31,151)( 32,152)
( 33,177)( 34,178)( 35,179)( 36,180)( 37,189)( 38,190)( 39,191)( 40,192)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,181)( 46,182)( 47,183)( 48,184)
( 49,209)( 50,210)( 51,211)( 52,212)( 53,221)( 54,222)( 55,223)( 56,224)
( 57,217)( 58,218)( 59,219)( 60,220)( 61,213)( 62,214)( 63,215)( 64,216)
( 65,193)( 66,194)( 67,195)( 68,196)( 69,205)( 70,206)( 71,207)( 72,208)
( 73,201)( 74,202)( 75,203)( 76,204)( 77,197)( 78,198)( 79,199)( 80,200)
( 81,225)( 82,226)( 83,227)( 84,228)( 85,237)( 86,238)( 87,239)( 88,240)
( 89,233)( 90,234)( 91,235)( 92,236)( 93,229)( 94,230)( 95,231)( 96,232)
( 97,257)( 98,258)( 99,259)(100,260)(101,269)(102,270)(103,271)(104,272)
(105,265)(106,266)(107,267)(108,268)(109,261)(110,262)(111,263)(112,264)
(113,241)(114,242)(115,243)(116,244)(117,253)(118,254)(119,255)(120,256)
(121,249)(122,250)(123,251)(124,252)(125,245)(126,246)(127,247)(128,248)
(129,273)(130,274)(131,275)(132,276)(133,285)(134,286)(135,287)(136,288)
(137,281)(138,282)(139,283)(140,284)(141,277)(142,278)(143,279)(144,280);;
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*s1*s2*s3*s1*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(288)!( 1,201)( 2,204)( 3,203)( 4,202)( 5,205)( 6,208)( 7,207)
( 8,206)( 9,193)( 10,196)( 11,195)( 12,194)( 13,197)( 14,200)( 15,199)
( 16,198)( 17,217)( 18,220)( 19,219)( 20,218)( 21,221)( 22,224)( 23,223)
( 24,222)( 25,209)( 26,212)( 27,211)( 28,210)( 29,213)( 30,216)( 31,215)
( 32,214)( 33,233)( 34,236)( 35,235)( 36,234)( 37,237)( 38,240)( 39,239)
( 40,238)( 41,225)( 42,228)( 43,227)( 44,226)( 45,229)( 46,232)( 47,231)
( 48,230)( 49,153)( 50,156)( 51,155)( 52,154)( 53,157)( 54,160)( 55,159)
( 56,158)( 57,145)( 58,148)( 59,147)( 60,146)( 61,149)( 62,152)( 63,151)
( 64,150)( 65,169)( 66,172)( 67,171)( 68,170)( 69,173)( 70,176)( 71,175)
( 72,174)( 73,161)( 74,164)( 75,163)( 76,162)( 77,165)( 78,168)( 79,167)
( 80,166)( 81,185)( 82,188)( 83,187)( 84,186)( 85,189)( 86,192)( 87,191)
( 88,190)( 89,177)( 90,180)( 91,179)( 92,178)( 93,181)( 94,184)( 95,183)
( 96,182)( 97,249)( 98,252)( 99,251)(100,250)(101,253)(102,256)(103,255)
(104,254)(105,241)(106,244)(107,243)(108,242)(109,245)(110,248)(111,247)
(112,246)(113,265)(114,268)(115,267)(116,266)(117,269)(118,272)(119,271)
(120,270)(121,257)(122,260)(123,259)(124,258)(125,261)(126,264)(127,263)
(128,262)(129,281)(130,284)(131,283)(132,282)(133,285)(134,288)(135,287)
(136,286)(137,273)(138,276)(139,275)(140,274)(141,277)(142,280)(143,279)
(144,278);
s2 := Sym(288)!( 1, 2)( 5, 6)( 9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 34)
( 18, 33)( 19, 35)( 20, 36)( 21, 38)( 22, 37)( 23, 39)( 24, 40)( 25, 46)
( 26, 45)( 27, 47)( 28, 48)( 29, 42)( 30, 41)( 31, 43)( 32, 44)( 49, 98)
( 50, 97)( 51, 99)( 52,100)( 53,102)( 54,101)( 55,103)( 56,104)( 57,110)
( 58,109)( 59,111)( 60,112)( 61,106)( 62,105)( 63,107)( 64,108)( 65,130)
( 66,129)( 67,131)( 68,132)( 69,134)( 70,133)( 71,135)( 72,136)( 73,142)
( 74,141)( 75,143)( 76,144)( 77,138)( 78,137)( 79,139)( 80,140)( 81,114)
( 82,113)( 83,115)( 84,116)( 85,118)( 86,117)( 87,119)( 88,120)( 89,126)
( 90,125)( 91,127)( 92,128)( 93,122)( 94,121)( 95,123)( 96,124)(145,146)
(149,150)(153,158)(154,157)(155,159)(156,160)(161,178)(162,177)(163,179)
(164,180)(165,182)(166,181)(167,183)(168,184)(169,190)(170,189)(171,191)
(172,192)(173,186)(174,185)(175,187)(176,188)(193,242)(194,241)(195,243)
(196,244)(197,246)(198,245)(199,247)(200,248)(201,254)(202,253)(203,255)
(204,256)(205,250)(206,249)(207,251)(208,252)(209,274)(210,273)(211,275)
(212,276)(213,278)(214,277)(215,279)(216,280)(217,286)(218,285)(219,287)
(220,288)(221,282)(222,281)(223,283)(224,284)(225,258)(226,257)(227,259)
(228,260)(229,262)(230,261)(231,263)(232,264)(233,270)(234,269)(235,271)
(236,272)(237,266)(238,265)(239,267)(240,268);
s3 := Sym(288)!( 1,161)( 2,162)( 3,163)( 4,164)( 5,173)( 6,174)( 7,175)
( 8,176)( 9,169)( 10,170)( 11,171)( 12,172)( 13,165)( 14,166)( 15,167)
( 16,168)( 17,145)( 18,146)( 19,147)( 20,148)( 21,157)( 22,158)( 23,159)
( 24,160)( 25,153)( 26,154)( 27,155)( 28,156)( 29,149)( 30,150)( 31,151)
( 32,152)( 33,177)( 34,178)( 35,179)( 36,180)( 37,189)( 38,190)( 39,191)
( 40,192)( 41,185)( 42,186)( 43,187)( 44,188)( 45,181)( 46,182)( 47,183)
( 48,184)( 49,209)( 50,210)( 51,211)( 52,212)( 53,221)( 54,222)( 55,223)
( 56,224)( 57,217)( 58,218)( 59,219)( 60,220)( 61,213)( 62,214)( 63,215)
( 64,216)( 65,193)( 66,194)( 67,195)( 68,196)( 69,205)( 70,206)( 71,207)
( 72,208)( 73,201)( 74,202)( 75,203)( 76,204)( 77,197)( 78,198)( 79,199)
( 80,200)( 81,225)( 82,226)( 83,227)( 84,228)( 85,237)( 86,238)( 87,239)
( 88,240)( 89,233)( 90,234)( 91,235)( 92,236)( 93,229)( 94,230)( 95,231)
( 96,232)( 97,257)( 98,258)( 99,259)(100,260)(101,269)(102,270)(103,271)
(104,272)(105,265)(106,266)(107,267)(108,268)(109,261)(110,262)(111,263)
(112,264)(113,241)(114,242)(115,243)(116,244)(117,253)(118,254)(119,255)
(120,256)(121,249)(122,250)(123,251)(124,252)(125,245)(126,246)(127,247)
(128,248)(129,273)(130,274)(131,275)(132,276)(133,285)(134,286)(135,287)
(136,288)(137,281)(138,282)(139,283)(140,284)(141,277)(142,278)(143,279)
(144,280);
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*s1*s2*s3*s1*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;
References : None.
to this polytope