Polytope of Type {2,2,12,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,12,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,157570)
Rank : 5
Schlafli Type : {2,2,12,3}
Number of vertices, edges, etc : 2, 2, 48, 72, 12
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
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 : {2,2,6,3}*576
3-fold quotients : {2,2,12,3}*384
6-fold quotients : {2,2,6,3}*192
8-fold quotients : {2,2,6,3}*144
12-fold quotients : {2,2,3,3}*96
24-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 77)( 6, 78)( 7, 81)( 8, 82)( 9, 79)( 10, 80)( 11, 84)( 12, 83)
( 13, 85)( 14, 86)( 15, 89)( 16, 90)( 17, 87)( 18, 88)( 19, 92)( 20, 91)
( 21, 93)( 22, 94)( 23, 97)( 24, 98)( 25, 95)( 26, 96)( 27,100)( 28, 99)
( 29,125)( 30,126)( 31,129)( 32,130)( 33,127)( 34,128)( 35,132)( 36,131)
( 37,133)( 38,134)( 39,137)( 40,138)( 41,135)( 42,136)( 43,140)( 44,139)
( 45,141)( 46,142)( 47,145)( 48,146)( 49,143)( 50,144)( 51,148)( 52,147)
( 53,101)( 54,102)( 55,105)( 56,106)( 57,103)( 58,104)( 59,108)( 60,107)
( 61,109)( 62,110)( 63,113)( 64,114)( 65,111)( 66,112)( 67,116)( 68,115)
( 69,117)( 70,118)( 71,121)( 72,122)( 73,119)( 74,120)( 75,124)( 76,123)
(149,221)(150,222)(151,225)(152,226)(153,223)(154,224)(155,228)(156,227)
(157,229)(158,230)(159,233)(160,234)(161,231)(162,232)(163,236)(164,235)
(165,237)(166,238)(167,241)(168,242)(169,239)(170,240)(171,244)(172,243)
(173,269)(174,270)(175,273)(176,274)(177,271)(178,272)(179,276)(180,275)
(181,277)(182,278)(183,281)(184,282)(185,279)(186,280)(187,284)(188,283)
(189,285)(190,286)(191,289)(192,290)(193,287)(194,288)(195,292)(196,291)
(197,245)(198,246)(199,249)(200,250)(201,247)(202,248)(203,252)(204,251)
(205,253)(206,254)(207,257)(208,258)(209,255)(210,256)(211,260)(212,259)
(213,261)(214,262)(215,265)(216,266)(217,263)(218,264)(219,268)(220,267);;
s3 := ( 5,245)( 6,246)( 7,248)( 8,247)( 9,251)( 10,252)( 11,249)( 12,250)
( 13,261)( 14,262)( 15,264)( 16,263)( 17,267)( 18,268)( 19,265)( 20,266)
( 21,253)( 22,254)( 23,256)( 24,255)( 25,259)( 26,260)( 27,257)( 28,258)
( 29,221)( 30,222)( 31,224)( 32,223)( 33,227)( 34,228)( 35,225)( 36,226)
( 37,237)( 38,238)( 39,240)( 40,239)( 41,243)( 42,244)( 43,241)( 44,242)
( 45,229)( 46,230)( 47,232)( 48,231)( 49,235)( 50,236)( 51,233)( 52,234)
( 53,269)( 54,270)( 55,272)( 56,271)( 57,275)( 58,276)( 59,273)( 60,274)
( 61,285)( 62,286)( 63,288)( 64,287)( 65,291)( 66,292)( 67,289)( 68,290)
( 69,277)( 70,278)( 71,280)( 72,279)( 73,283)( 74,284)( 75,281)( 76,282)
( 77,174)( 78,173)( 79,175)( 80,176)( 81,180)( 82,179)( 83,178)( 84,177)
( 85,190)( 86,189)( 87,191)( 88,192)( 89,196)( 90,195)( 91,194)( 92,193)
( 93,182)( 94,181)( 95,183)( 96,184)( 97,188)( 98,187)( 99,186)(100,185)
(101,150)(102,149)(103,151)(104,152)(105,156)(106,155)(107,154)(108,153)
(109,166)(110,165)(111,167)(112,168)(113,172)(114,171)(115,170)(116,169)
(117,158)(118,157)(119,159)(120,160)(121,164)(122,163)(123,162)(124,161)
(125,198)(126,197)(127,199)(128,200)(129,204)(130,203)(131,202)(132,201)
(133,214)(134,213)(135,215)(136,216)(137,220)(138,219)(139,218)(140,217)
(141,206)(142,205)(143,207)(144,208)(145,212)(146,211)(147,210)(148,209);;
s4 := ( 5,235)( 6,236)( 7,232)( 8,231)( 9,233)( 10,234)( 11,229)( 12,230)
( 13,227)( 14,228)( 15,224)( 16,223)( 17,225)( 18,226)( 19,221)( 20,222)
( 21,243)( 22,244)( 23,240)( 24,239)( 25,241)( 26,242)( 27,237)( 28,238)
( 29,283)( 30,284)( 31,280)( 32,279)( 33,281)( 34,282)( 35,277)( 36,278)
( 37,275)( 38,276)( 39,272)( 40,271)( 41,273)( 42,274)( 43,269)( 44,270)
( 45,291)( 46,292)( 47,288)( 48,287)( 49,289)( 50,290)( 51,285)( 52,286)
( 53,259)( 54,260)( 55,256)( 56,255)( 57,257)( 58,258)( 59,253)( 60,254)
( 61,251)( 62,252)( 63,248)( 64,247)( 65,249)( 66,250)( 67,245)( 68,246)
( 69,267)( 70,268)( 71,264)( 72,263)( 73,265)( 74,266)( 75,261)( 76,262)
( 77,164)( 78,163)( 79,159)( 80,160)( 81,162)( 82,161)( 83,158)( 84,157)
( 85,156)( 86,155)( 87,151)( 88,152)( 89,154)( 90,153)( 91,150)( 92,149)
( 93,172)( 94,171)( 95,167)( 96,168)( 97,170)( 98,169)( 99,166)(100,165)
(101,212)(102,211)(103,207)(104,208)(105,210)(106,209)(107,206)(108,205)
(109,204)(110,203)(111,199)(112,200)(113,202)(114,201)(115,198)(116,197)
(117,220)(118,219)(119,215)(120,216)(121,218)(122,217)(123,214)(124,213)
(125,188)(126,187)(127,183)(128,184)(129,186)(130,185)(131,182)(132,181)
(133,180)(134,179)(135,175)(136,176)(137,178)(138,177)(139,174)(140,173)
(141,196)(142,195)(143,191)(144,192)(145,194)(146,193)(147,190)(148,189);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(292)!(1,2);
s1 := Sym(292)!(3,4);
s2 := Sym(292)!( 5, 77)( 6, 78)( 7, 81)( 8, 82)( 9, 79)( 10, 80)( 11, 84)
( 12, 83)( 13, 85)( 14, 86)( 15, 89)( 16, 90)( 17, 87)( 18, 88)( 19, 92)
( 20, 91)( 21, 93)( 22, 94)( 23, 97)( 24, 98)( 25, 95)( 26, 96)( 27,100)
( 28, 99)( 29,125)( 30,126)( 31,129)( 32,130)( 33,127)( 34,128)( 35,132)
( 36,131)( 37,133)( 38,134)( 39,137)( 40,138)( 41,135)( 42,136)( 43,140)
( 44,139)( 45,141)( 46,142)( 47,145)( 48,146)( 49,143)( 50,144)( 51,148)
( 52,147)( 53,101)( 54,102)( 55,105)( 56,106)( 57,103)( 58,104)( 59,108)
( 60,107)( 61,109)( 62,110)( 63,113)( 64,114)( 65,111)( 66,112)( 67,116)
( 68,115)( 69,117)( 70,118)( 71,121)( 72,122)( 73,119)( 74,120)( 75,124)
( 76,123)(149,221)(150,222)(151,225)(152,226)(153,223)(154,224)(155,228)
(156,227)(157,229)(158,230)(159,233)(160,234)(161,231)(162,232)(163,236)
(164,235)(165,237)(166,238)(167,241)(168,242)(169,239)(170,240)(171,244)
(172,243)(173,269)(174,270)(175,273)(176,274)(177,271)(178,272)(179,276)
(180,275)(181,277)(182,278)(183,281)(184,282)(185,279)(186,280)(187,284)
(188,283)(189,285)(190,286)(191,289)(192,290)(193,287)(194,288)(195,292)
(196,291)(197,245)(198,246)(199,249)(200,250)(201,247)(202,248)(203,252)
(204,251)(205,253)(206,254)(207,257)(208,258)(209,255)(210,256)(211,260)
(212,259)(213,261)(214,262)(215,265)(216,266)(217,263)(218,264)(219,268)
(220,267);
s3 := Sym(292)!( 5,245)( 6,246)( 7,248)( 8,247)( 9,251)( 10,252)( 11,249)
( 12,250)( 13,261)( 14,262)( 15,264)( 16,263)( 17,267)( 18,268)( 19,265)
( 20,266)( 21,253)( 22,254)( 23,256)( 24,255)( 25,259)( 26,260)( 27,257)
( 28,258)( 29,221)( 30,222)( 31,224)( 32,223)( 33,227)( 34,228)( 35,225)
( 36,226)( 37,237)( 38,238)( 39,240)( 40,239)( 41,243)( 42,244)( 43,241)
( 44,242)( 45,229)( 46,230)( 47,232)( 48,231)( 49,235)( 50,236)( 51,233)
( 52,234)( 53,269)( 54,270)( 55,272)( 56,271)( 57,275)( 58,276)( 59,273)
( 60,274)( 61,285)( 62,286)( 63,288)( 64,287)( 65,291)( 66,292)( 67,289)
( 68,290)( 69,277)( 70,278)( 71,280)( 72,279)( 73,283)( 74,284)( 75,281)
( 76,282)( 77,174)( 78,173)( 79,175)( 80,176)( 81,180)( 82,179)( 83,178)
( 84,177)( 85,190)( 86,189)( 87,191)( 88,192)( 89,196)( 90,195)( 91,194)
( 92,193)( 93,182)( 94,181)( 95,183)( 96,184)( 97,188)( 98,187)( 99,186)
(100,185)(101,150)(102,149)(103,151)(104,152)(105,156)(106,155)(107,154)
(108,153)(109,166)(110,165)(111,167)(112,168)(113,172)(114,171)(115,170)
(116,169)(117,158)(118,157)(119,159)(120,160)(121,164)(122,163)(123,162)
(124,161)(125,198)(126,197)(127,199)(128,200)(129,204)(130,203)(131,202)
(132,201)(133,214)(134,213)(135,215)(136,216)(137,220)(138,219)(139,218)
(140,217)(141,206)(142,205)(143,207)(144,208)(145,212)(146,211)(147,210)
(148,209);
s4 := Sym(292)!( 5,235)( 6,236)( 7,232)( 8,231)( 9,233)( 10,234)( 11,229)
( 12,230)( 13,227)( 14,228)( 15,224)( 16,223)( 17,225)( 18,226)( 19,221)
( 20,222)( 21,243)( 22,244)( 23,240)( 24,239)( 25,241)( 26,242)( 27,237)
( 28,238)( 29,283)( 30,284)( 31,280)( 32,279)( 33,281)( 34,282)( 35,277)
( 36,278)( 37,275)( 38,276)( 39,272)( 40,271)( 41,273)( 42,274)( 43,269)
( 44,270)( 45,291)( 46,292)( 47,288)( 48,287)( 49,289)( 50,290)( 51,285)
( 52,286)( 53,259)( 54,260)( 55,256)( 56,255)( 57,257)( 58,258)( 59,253)
( 60,254)( 61,251)( 62,252)( 63,248)( 64,247)( 65,249)( 66,250)( 67,245)
( 68,246)( 69,267)( 70,268)( 71,264)( 72,263)( 73,265)( 74,266)( 75,261)
( 76,262)( 77,164)( 78,163)( 79,159)( 80,160)( 81,162)( 82,161)( 83,158)
( 84,157)( 85,156)( 86,155)( 87,151)( 88,152)( 89,154)( 90,153)( 91,150)
( 92,149)( 93,172)( 94,171)( 95,167)( 96,168)( 97,170)( 98,169)( 99,166)
(100,165)(101,212)(102,211)(103,207)(104,208)(105,210)(106,209)(107,206)
(108,205)(109,204)(110,203)(111,199)(112,200)(113,202)(114,201)(115,198)
(116,197)(117,220)(118,219)(119,215)(120,216)(121,218)(122,217)(123,214)
(124,213)(125,188)(126,187)(127,183)(128,184)(129,186)(130,185)(131,182)
(132,181)(133,180)(134,179)(135,175)(136,176)(137,178)(138,177)(139,174)
(140,173)(141,196)(142,195)(143,191)(144,192)(145,194)(146,193)(147,190)
(148,189);
poly := sub<Sym(292)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4, s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s3 >;
to this polytope