Polytope of Type {2,3,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,12}*576
if this polytope has a name.
Group : SmallGroup(576,8319)
Rank : 4
Schlafli Type : {2,3,12}
Number of vertices, edges, etc : 2, 12, 72, 48
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,3,12,2} of size 1152
Vertex Figure Of :
{2,2,3,12} of size 1152
{3,2,3,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,3,6}*288
3-fold quotients : {2,3,12}*192
6-fold quotients : {2,3,6}*96
8-fold quotients : {2,3,6}*72
12-fold quotients : {2,3,3}*48
24-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,6,12}*1152c
3-fold covers : {2,9,12}*1728, {2,3,12}*1728, {6,3,12}*1728
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,219)( 4,220)( 5,223)( 6,224)( 7,221)( 8,222)( 9,226)( 10,225)
( 11,235)( 12,236)( 13,239)( 14,240)( 15,237)( 16,238)( 17,242)( 18,241)
( 19,227)( 20,228)( 21,231)( 22,232)( 23,229)( 24,230)( 25,234)( 26,233)
( 27,267)( 28,268)( 29,271)( 30,272)( 31,269)( 32,270)( 33,274)( 34,273)
( 35,283)( 36,284)( 37,287)( 38,288)( 39,285)( 40,286)( 41,290)( 42,289)
( 43,275)( 44,276)( 45,279)( 46,280)( 47,277)( 48,278)( 49,282)( 50,281)
( 51,243)( 52,244)( 53,247)( 54,248)( 55,245)( 56,246)( 57,250)( 58,249)
( 59,259)( 60,260)( 61,263)( 62,264)( 63,261)( 64,262)( 65,266)( 66,265)
( 67,251)( 68,252)( 69,255)( 70,256)( 71,253)( 72,254)( 73,258)( 74,257)
( 75,148)( 76,147)( 77,152)( 78,151)( 79,150)( 80,149)( 81,153)( 82,154)
( 83,164)( 84,163)( 85,168)( 86,167)( 87,166)( 88,165)( 89,169)( 90,170)
( 91,156)( 92,155)( 93,160)( 94,159)( 95,158)( 96,157)( 97,161)( 98,162)
( 99,196)(100,195)(101,200)(102,199)(103,198)(104,197)(105,201)(106,202)
(107,212)(108,211)(109,216)(110,215)(111,214)(112,213)(113,217)(114,218)
(115,204)(116,203)(117,208)(118,207)(119,206)(120,205)(121,209)(122,210)
(123,172)(124,171)(125,176)(126,175)(127,174)(128,173)(129,177)(130,178)
(131,188)(132,187)(133,192)(134,191)(135,190)(136,189)(137,193)(138,194)
(139,180)(140,179)(141,184)(142,183)(143,182)(144,181)(145,185)(146,186);;
s2 := ( 3,251)( 4,252)( 5,254)( 6,253)( 7,257)( 8,258)( 9,255)( 10,256)
( 11,243)( 12,244)( 13,246)( 14,245)( 15,249)( 16,250)( 17,247)( 18,248)
( 19,259)( 20,260)( 21,262)( 22,261)( 23,265)( 24,266)( 25,263)( 26,264)
( 27,227)( 28,228)( 29,230)( 30,229)( 31,233)( 32,234)( 33,231)( 34,232)
( 35,219)( 36,220)( 37,222)( 38,221)( 39,225)( 40,226)( 41,223)( 42,224)
( 43,235)( 44,236)( 45,238)( 46,237)( 47,241)( 48,242)( 49,239)( 50,240)
( 51,275)( 52,276)( 53,278)( 54,277)( 55,281)( 56,282)( 57,279)( 58,280)
( 59,267)( 60,268)( 61,270)( 62,269)( 63,273)( 64,274)( 65,271)( 66,272)
( 67,283)( 68,284)( 69,286)( 70,285)( 71,289)( 72,290)( 73,287)( 74,288)
( 75,180)( 76,179)( 77,181)( 78,182)( 79,186)( 80,185)( 81,184)( 82,183)
( 83,172)( 84,171)( 85,173)( 86,174)( 87,178)( 88,177)( 89,176)( 90,175)
( 91,188)( 92,187)( 93,189)( 94,190)( 95,194)( 96,193)( 97,192)( 98,191)
( 99,156)(100,155)(101,157)(102,158)(103,162)(104,161)(105,160)(106,159)
(107,148)(108,147)(109,149)(110,150)(111,154)(112,153)(113,152)(114,151)
(115,164)(116,163)(117,165)(118,166)(119,170)(120,169)(121,168)(122,167)
(123,204)(124,203)(125,205)(126,206)(127,210)(128,209)(129,208)(130,207)
(131,196)(132,195)(133,197)(134,198)(135,202)(136,201)(137,200)(138,199)
(139,212)(140,211)(141,213)(142,214)(143,218)(144,217)(145,216)(146,215);;
s3 := ( 3, 81)( 4, 82)( 5, 78)( 6, 77)( 7, 79)( 8, 80)( 9, 75)( 10, 76)
( 11, 89)( 12, 90)( 13, 86)( 14, 85)( 15, 87)( 16, 88)( 17, 83)( 18, 84)
( 19, 97)( 20, 98)( 21, 94)( 22, 93)( 23, 95)( 24, 96)( 25, 91)( 26, 92)
( 27,129)( 28,130)( 29,126)( 30,125)( 31,127)( 32,128)( 33,123)( 34,124)
( 35,137)( 36,138)( 37,134)( 38,133)( 39,135)( 40,136)( 41,131)( 42,132)
( 43,145)( 44,146)( 45,142)( 46,141)( 47,143)( 48,144)( 49,139)( 50,140)
( 51,105)( 52,106)( 53,102)( 54,101)( 55,103)( 56,104)( 57, 99)( 58,100)
( 59,113)( 60,114)( 61,110)( 62,109)( 63,111)( 64,112)( 65,107)( 66,108)
( 67,121)( 68,122)( 69,118)( 70,117)( 71,119)( 72,120)( 73,115)( 74,116)
(147,225)(148,226)(149,222)(150,221)(151,223)(152,224)(153,219)(154,220)
(155,233)(156,234)(157,230)(158,229)(159,231)(160,232)(161,227)(162,228)
(163,241)(164,242)(165,238)(166,237)(167,239)(168,240)(169,235)(170,236)
(171,273)(172,274)(173,270)(174,269)(175,271)(176,272)(177,267)(178,268)
(179,281)(180,282)(181,278)(182,277)(183,279)(184,280)(185,275)(186,276)
(187,289)(188,290)(189,286)(190,285)(191,287)(192,288)(193,283)(194,284)
(195,249)(196,250)(197,246)(198,245)(199,247)(200,248)(201,243)(202,244)
(203,257)(204,258)(205,254)(206,253)(207,255)(208,256)(209,251)(210,252)
(211,265)(212,266)(213,262)(214,261)(215,263)(216,264)(217,259)(218,260);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(290)!(1,2);
s1 := Sym(290)!( 3,219)( 4,220)( 5,223)( 6,224)( 7,221)( 8,222)( 9,226)
( 10,225)( 11,235)( 12,236)( 13,239)( 14,240)( 15,237)( 16,238)( 17,242)
( 18,241)( 19,227)( 20,228)( 21,231)( 22,232)( 23,229)( 24,230)( 25,234)
( 26,233)( 27,267)( 28,268)( 29,271)( 30,272)( 31,269)( 32,270)( 33,274)
( 34,273)( 35,283)( 36,284)( 37,287)( 38,288)( 39,285)( 40,286)( 41,290)
( 42,289)( 43,275)( 44,276)( 45,279)( 46,280)( 47,277)( 48,278)( 49,282)
( 50,281)( 51,243)( 52,244)( 53,247)( 54,248)( 55,245)( 56,246)( 57,250)
( 58,249)( 59,259)( 60,260)( 61,263)( 62,264)( 63,261)( 64,262)( 65,266)
( 66,265)( 67,251)( 68,252)( 69,255)( 70,256)( 71,253)( 72,254)( 73,258)
( 74,257)( 75,148)( 76,147)( 77,152)( 78,151)( 79,150)( 80,149)( 81,153)
( 82,154)( 83,164)( 84,163)( 85,168)( 86,167)( 87,166)( 88,165)( 89,169)
( 90,170)( 91,156)( 92,155)( 93,160)( 94,159)( 95,158)( 96,157)( 97,161)
( 98,162)( 99,196)(100,195)(101,200)(102,199)(103,198)(104,197)(105,201)
(106,202)(107,212)(108,211)(109,216)(110,215)(111,214)(112,213)(113,217)
(114,218)(115,204)(116,203)(117,208)(118,207)(119,206)(120,205)(121,209)
(122,210)(123,172)(124,171)(125,176)(126,175)(127,174)(128,173)(129,177)
(130,178)(131,188)(132,187)(133,192)(134,191)(135,190)(136,189)(137,193)
(138,194)(139,180)(140,179)(141,184)(142,183)(143,182)(144,181)(145,185)
(146,186);
s2 := Sym(290)!( 3,251)( 4,252)( 5,254)( 6,253)( 7,257)( 8,258)( 9,255)
( 10,256)( 11,243)( 12,244)( 13,246)( 14,245)( 15,249)( 16,250)( 17,247)
( 18,248)( 19,259)( 20,260)( 21,262)( 22,261)( 23,265)( 24,266)( 25,263)
( 26,264)( 27,227)( 28,228)( 29,230)( 30,229)( 31,233)( 32,234)( 33,231)
( 34,232)( 35,219)( 36,220)( 37,222)( 38,221)( 39,225)( 40,226)( 41,223)
( 42,224)( 43,235)( 44,236)( 45,238)( 46,237)( 47,241)( 48,242)( 49,239)
( 50,240)( 51,275)( 52,276)( 53,278)( 54,277)( 55,281)( 56,282)( 57,279)
( 58,280)( 59,267)( 60,268)( 61,270)( 62,269)( 63,273)( 64,274)( 65,271)
( 66,272)( 67,283)( 68,284)( 69,286)( 70,285)( 71,289)( 72,290)( 73,287)
( 74,288)( 75,180)( 76,179)( 77,181)( 78,182)( 79,186)( 80,185)( 81,184)
( 82,183)( 83,172)( 84,171)( 85,173)( 86,174)( 87,178)( 88,177)( 89,176)
( 90,175)( 91,188)( 92,187)( 93,189)( 94,190)( 95,194)( 96,193)( 97,192)
( 98,191)( 99,156)(100,155)(101,157)(102,158)(103,162)(104,161)(105,160)
(106,159)(107,148)(108,147)(109,149)(110,150)(111,154)(112,153)(113,152)
(114,151)(115,164)(116,163)(117,165)(118,166)(119,170)(120,169)(121,168)
(122,167)(123,204)(124,203)(125,205)(126,206)(127,210)(128,209)(129,208)
(130,207)(131,196)(132,195)(133,197)(134,198)(135,202)(136,201)(137,200)
(138,199)(139,212)(140,211)(141,213)(142,214)(143,218)(144,217)(145,216)
(146,215);
s3 := Sym(290)!( 3, 81)( 4, 82)( 5, 78)( 6, 77)( 7, 79)( 8, 80)( 9, 75)
( 10, 76)( 11, 89)( 12, 90)( 13, 86)( 14, 85)( 15, 87)( 16, 88)( 17, 83)
( 18, 84)( 19, 97)( 20, 98)( 21, 94)( 22, 93)( 23, 95)( 24, 96)( 25, 91)
( 26, 92)( 27,129)( 28,130)( 29,126)( 30,125)( 31,127)( 32,128)( 33,123)
( 34,124)( 35,137)( 36,138)( 37,134)( 38,133)( 39,135)( 40,136)( 41,131)
( 42,132)( 43,145)( 44,146)( 45,142)( 46,141)( 47,143)( 48,144)( 49,139)
( 50,140)( 51,105)( 52,106)( 53,102)( 54,101)( 55,103)( 56,104)( 57, 99)
( 58,100)( 59,113)( 60,114)( 61,110)( 62,109)( 63,111)( 64,112)( 65,107)
( 66,108)( 67,121)( 68,122)( 69,118)( 70,117)( 71,119)( 72,120)( 73,115)
( 74,116)(147,225)(148,226)(149,222)(150,221)(151,223)(152,224)(153,219)
(154,220)(155,233)(156,234)(157,230)(158,229)(159,231)(160,232)(161,227)
(162,228)(163,241)(164,242)(165,238)(166,237)(167,239)(168,240)(169,235)
(170,236)(171,273)(172,274)(173,270)(174,269)(175,271)(176,272)(177,267)
(178,268)(179,281)(180,282)(181,278)(182,277)(183,279)(184,280)(185,275)
(186,276)(187,289)(188,290)(189,286)(190,285)(191,287)(192,288)(193,283)
(194,284)(195,249)(196,250)(197,246)(198,245)(199,247)(200,248)(201,243)
(202,244)(203,257)(204,258)(205,254)(206,253)(207,255)(208,256)(209,251)
(210,252)(211,265)(212,266)(213,262)(214,261)(215,263)(216,264)(217,259)
(218,260);
poly := sub<Sym(290)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2 >;
to this polytope