Polytope of Type {2,12,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,8}*1152b
if this polytope has a name.
Group : SmallGroup(1152,98809)
Rank : 4
Schlafli Type : {2,12,8}
Number of vertices, edges, etc : 2, 36, 144, 24
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 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 : {2,12,4}*576
4-fold quotients : {2,6,4}*288
8-fold quotients : {2,6,4}*144
9-fold quotients : {2,4,8}*128b
18-fold quotients : {2,4,4}*64
36-fold quotients : {2,2,4}*32, {2,4,2}*32
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,111)( 4,113)( 5,112)( 6,117)( 7,119)( 8,118)( 9,114)( 10,116)
( 11,115)( 12,120)( 13,122)( 14,121)( 15,126)( 16,128)( 17,127)( 18,123)
( 19,125)( 20,124)( 21,129)( 22,131)( 23,130)( 24,135)( 25,137)( 26,136)
( 27,132)( 28,134)( 29,133)( 30,138)( 31,140)( 32,139)( 33,144)( 34,146)
( 35,145)( 36,141)( 37,143)( 38,142)( 39, 75)( 40, 77)( 41, 76)( 42, 81)
( 43, 83)( 44, 82)( 45, 78)( 46, 80)( 47, 79)( 48, 84)( 49, 86)( 50, 85)
( 51, 90)( 52, 92)( 53, 91)( 54, 87)( 55, 89)( 56, 88)( 57, 93)( 58, 95)
( 59, 94)( 60, 99)( 61,101)( 62,100)( 63, 96)( 64, 98)( 65, 97)( 66,102)
( 67,104)( 68,103)( 69,108)( 70,110)( 71,109)( 72,105)( 73,107)( 74,106)
(147,255)(148,257)(149,256)(150,261)(151,263)(152,262)(153,258)(154,260)
(155,259)(156,264)(157,266)(158,265)(159,270)(160,272)(161,271)(162,267)
(163,269)(164,268)(165,273)(166,275)(167,274)(168,279)(169,281)(170,280)
(171,276)(172,278)(173,277)(174,282)(175,284)(176,283)(177,288)(178,290)
(179,289)(180,285)(181,287)(182,286)(183,219)(184,221)(185,220)(186,225)
(187,227)(188,226)(189,222)(190,224)(191,223)(192,228)(193,230)(194,229)
(195,234)(196,236)(197,235)(198,231)(199,233)(200,232)(201,237)(202,239)
(203,238)(204,243)(205,245)(206,244)(207,240)(208,242)(209,241)(210,246)
(211,248)(212,247)(213,252)(214,254)(215,253)(216,249)(217,251)(218,250);;
s2 := ( 3,187)( 4,184)( 5,190)( 6,186)( 7,183)( 8,189)( 9,188)( 10,185)
( 11,191)( 12,196)( 13,193)( 14,199)( 15,195)( 16,192)( 17,198)( 18,197)
( 19,194)( 20,200)( 21,205)( 22,202)( 23,208)( 24,204)( 25,201)( 26,207)
( 27,206)( 28,203)( 29,209)( 30,214)( 31,211)( 32,217)( 33,213)( 34,210)
( 35,216)( 36,215)( 37,212)( 38,218)( 39,151)( 40,148)( 41,154)( 42,150)
( 43,147)( 44,153)( 45,152)( 46,149)( 47,155)( 48,160)( 49,157)( 50,163)
( 51,159)( 52,156)( 53,162)( 54,161)( 55,158)( 56,164)( 57,169)( 58,166)
( 59,172)( 60,168)( 61,165)( 62,171)( 63,170)( 64,167)( 65,173)( 66,178)
( 67,175)( 68,181)( 69,177)( 70,174)( 71,180)( 72,179)( 73,176)( 74,182)
( 75,277)( 76,274)( 77,280)( 78,276)( 79,273)( 80,279)( 81,278)( 82,275)
( 83,281)( 84,286)( 85,283)( 86,289)( 87,285)( 88,282)( 89,288)( 90,287)
( 91,284)( 92,290)( 93,259)( 94,256)( 95,262)( 96,258)( 97,255)( 98,261)
( 99,260)(100,257)(101,263)(102,268)(103,265)(104,271)(105,267)(106,264)
(107,270)(108,269)(109,266)(110,272)(111,241)(112,238)(113,244)(114,240)
(115,237)(116,243)(117,242)(118,239)(119,245)(120,250)(121,247)(122,253)
(123,249)(124,246)(125,252)(126,251)(127,248)(128,254)(129,223)(130,220)
(131,226)(132,222)(133,219)(134,225)(135,224)(136,221)(137,227)(138,232)
(139,229)(140,235)(141,231)(142,228)(143,234)(144,233)(145,230)(146,236);;
s3 := ( 3, 75)( 4, 76)( 5, 77)( 6, 81)( 7, 82)( 8, 83)( 9, 78)( 10, 79)
( 11, 80)( 12, 84)( 13, 85)( 14, 86)( 15, 90)( 16, 91)( 17, 92)( 18, 87)
( 19, 88)( 20, 89)( 21,102)( 22,103)( 23,104)( 24,108)( 25,109)( 26,110)
( 27,105)( 28,106)( 29,107)( 30, 93)( 31, 94)( 32, 95)( 33, 99)( 34,100)
( 35,101)( 36, 96)( 37, 97)( 38, 98)( 39,111)( 40,112)( 41,113)( 42,117)
( 43,118)( 44,119)( 45,114)( 46,115)( 47,116)( 48,120)( 49,121)( 50,122)
( 51,126)( 52,127)( 53,128)( 54,123)( 55,124)( 56,125)( 57,138)( 58,139)
( 59,140)( 60,144)( 61,145)( 62,146)( 63,141)( 64,142)( 65,143)( 66,129)
( 67,130)( 68,131)( 69,135)( 70,136)( 71,137)( 72,132)( 73,133)( 74,134)
(147,264)(148,265)(149,266)(150,270)(151,271)(152,272)(153,267)(154,268)
(155,269)(156,255)(157,256)(158,257)(159,261)(160,262)(161,263)(162,258)
(163,259)(164,260)(165,273)(166,274)(167,275)(168,279)(169,280)(170,281)
(171,276)(172,277)(173,278)(174,282)(175,283)(176,284)(177,288)(178,289)
(179,290)(180,285)(181,286)(182,287)(183,219)(184,220)(185,221)(186,225)
(187,226)(188,227)(189,222)(190,223)(191,224)(192,228)(193,229)(194,230)
(195,234)(196,235)(197,236)(198,231)(199,232)(200,233)(201,246)(202,247)
(203,248)(204,252)(205,253)(206,254)(207,249)(208,250)(209,251)(210,237)
(211,238)(212,239)(213,243)(214,244)(215,245)(216,240)(217,241)(218,242);;
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,
s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(290)!(1,2);
s1 := Sym(290)!( 3,111)( 4,113)( 5,112)( 6,117)( 7,119)( 8,118)( 9,114)
( 10,116)( 11,115)( 12,120)( 13,122)( 14,121)( 15,126)( 16,128)( 17,127)
( 18,123)( 19,125)( 20,124)( 21,129)( 22,131)( 23,130)( 24,135)( 25,137)
( 26,136)( 27,132)( 28,134)( 29,133)( 30,138)( 31,140)( 32,139)( 33,144)
( 34,146)( 35,145)( 36,141)( 37,143)( 38,142)( 39, 75)( 40, 77)( 41, 76)
( 42, 81)( 43, 83)( 44, 82)( 45, 78)( 46, 80)( 47, 79)( 48, 84)( 49, 86)
( 50, 85)( 51, 90)( 52, 92)( 53, 91)( 54, 87)( 55, 89)( 56, 88)( 57, 93)
( 58, 95)( 59, 94)( 60, 99)( 61,101)( 62,100)( 63, 96)( 64, 98)( 65, 97)
( 66,102)( 67,104)( 68,103)( 69,108)( 70,110)( 71,109)( 72,105)( 73,107)
( 74,106)(147,255)(148,257)(149,256)(150,261)(151,263)(152,262)(153,258)
(154,260)(155,259)(156,264)(157,266)(158,265)(159,270)(160,272)(161,271)
(162,267)(163,269)(164,268)(165,273)(166,275)(167,274)(168,279)(169,281)
(170,280)(171,276)(172,278)(173,277)(174,282)(175,284)(176,283)(177,288)
(178,290)(179,289)(180,285)(181,287)(182,286)(183,219)(184,221)(185,220)
(186,225)(187,227)(188,226)(189,222)(190,224)(191,223)(192,228)(193,230)
(194,229)(195,234)(196,236)(197,235)(198,231)(199,233)(200,232)(201,237)
(202,239)(203,238)(204,243)(205,245)(206,244)(207,240)(208,242)(209,241)
(210,246)(211,248)(212,247)(213,252)(214,254)(215,253)(216,249)(217,251)
(218,250);
s2 := Sym(290)!( 3,187)( 4,184)( 5,190)( 6,186)( 7,183)( 8,189)( 9,188)
( 10,185)( 11,191)( 12,196)( 13,193)( 14,199)( 15,195)( 16,192)( 17,198)
( 18,197)( 19,194)( 20,200)( 21,205)( 22,202)( 23,208)( 24,204)( 25,201)
( 26,207)( 27,206)( 28,203)( 29,209)( 30,214)( 31,211)( 32,217)( 33,213)
( 34,210)( 35,216)( 36,215)( 37,212)( 38,218)( 39,151)( 40,148)( 41,154)
( 42,150)( 43,147)( 44,153)( 45,152)( 46,149)( 47,155)( 48,160)( 49,157)
( 50,163)( 51,159)( 52,156)( 53,162)( 54,161)( 55,158)( 56,164)( 57,169)
( 58,166)( 59,172)( 60,168)( 61,165)( 62,171)( 63,170)( 64,167)( 65,173)
( 66,178)( 67,175)( 68,181)( 69,177)( 70,174)( 71,180)( 72,179)( 73,176)
( 74,182)( 75,277)( 76,274)( 77,280)( 78,276)( 79,273)( 80,279)( 81,278)
( 82,275)( 83,281)( 84,286)( 85,283)( 86,289)( 87,285)( 88,282)( 89,288)
( 90,287)( 91,284)( 92,290)( 93,259)( 94,256)( 95,262)( 96,258)( 97,255)
( 98,261)( 99,260)(100,257)(101,263)(102,268)(103,265)(104,271)(105,267)
(106,264)(107,270)(108,269)(109,266)(110,272)(111,241)(112,238)(113,244)
(114,240)(115,237)(116,243)(117,242)(118,239)(119,245)(120,250)(121,247)
(122,253)(123,249)(124,246)(125,252)(126,251)(127,248)(128,254)(129,223)
(130,220)(131,226)(132,222)(133,219)(134,225)(135,224)(136,221)(137,227)
(138,232)(139,229)(140,235)(141,231)(142,228)(143,234)(144,233)(145,230)
(146,236);
s3 := Sym(290)!( 3, 75)( 4, 76)( 5, 77)( 6, 81)( 7, 82)( 8, 83)( 9, 78)
( 10, 79)( 11, 80)( 12, 84)( 13, 85)( 14, 86)( 15, 90)( 16, 91)( 17, 92)
( 18, 87)( 19, 88)( 20, 89)( 21,102)( 22,103)( 23,104)( 24,108)( 25,109)
( 26,110)( 27,105)( 28,106)( 29,107)( 30, 93)( 31, 94)( 32, 95)( 33, 99)
( 34,100)( 35,101)( 36, 96)( 37, 97)( 38, 98)( 39,111)( 40,112)( 41,113)
( 42,117)( 43,118)( 44,119)( 45,114)( 46,115)( 47,116)( 48,120)( 49,121)
( 50,122)( 51,126)( 52,127)( 53,128)( 54,123)( 55,124)( 56,125)( 57,138)
( 58,139)( 59,140)( 60,144)( 61,145)( 62,146)( 63,141)( 64,142)( 65,143)
( 66,129)( 67,130)( 68,131)( 69,135)( 70,136)( 71,137)( 72,132)( 73,133)
( 74,134)(147,264)(148,265)(149,266)(150,270)(151,271)(152,272)(153,267)
(154,268)(155,269)(156,255)(157,256)(158,257)(159,261)(160,262)(161,263)
(162,258)(163,259)(164,260)(165,273)(166,274)(167,275)(168,279)(169,280)
(170,281)(171,276)(172,277)(173,278)(174,282)(175,283)(176,284)(177,288)
(178,289)(179,290)(180,285)(181,286)(182,287)(183,219)(184,220)(185,221)
(186,225)(187,226)(188,227)(189,222)(190,223)(191,224)(192,228)(193,229)
(194,230)(195,234)(196,235)(197,236)(198,231)(199,232)(200,233)(201,246)
(202,247)(203,248)(204,252)(205,253)(206,254)(207,249)(208,250)(209,251)
(210,237)(211,238)(212,239)(213,243)(214,244)(215,245)(216,240)(217,241)
(218,242);
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, s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope