Polytope of Type {22,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,6,4}*1056b
if this polytope has a name.
Group : SmallGroup(1056,1015)
Rank : 4
Schlafli Type : {22,6,4}
Number of vertices, edges, etc : 22, 66, 12, 4
Order of s0s1s2s3 : 66
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) :
11-fold quotients : {2,6,4}*96c
22-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 41)( 6, 42)( 7, 43)( 8, 44)( 9, 37)( 10, 38)( 11, 39)( 12, 40)
( 13, 33)( 14, 34)( 15, 35)( 16, 36)( 17, 29)( 18, 30)( 19, 31)( 20, 32)
( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 49, 85)( 50, 86)( 51, 87)( 52, 88)
( 53, 81)( 54, 82)( 55, 83)( 56, 84)( 57, 77)( 58, 78)( 59, 79)( 60, 80)
( 61, 73)( 62, 74)( 63, 75)( 64, 76)( 65, 69)( 66, 70)( 67, 71)( 68, 72)
( 93,129)( 94,130)( 95,131)( 96,132)( 97,125)( 98,126)( 99,127)(100,128)
(101,121)(102,122)(103,123)(104,124)(105,117)(106,118)(107,119)(108,120)
(109,113)(110,114)(111,115)(112,116)(137,173)(138,174)(139,175)(140,176)
(141,169)(142,170)(143,171)(144,172)(145,165)(146,166)(147,167)(148,168)
(149,161)(150,162)(151,163)(152,164)(153,157)(154,158)(155,159)(156,160)
(181,217)(182,218)(183,219)(184,220)(185,213)(186,214)(187,215)(188,216)
(189,209)(190,210)(191,211)(192,212)(193,205)(194,206)(195,207)(196,208)
(197,201)(198,202)(199,203)(200,204)(225,261)(226,262)(227,263)(228,264)
(229,257)(230,258)(231,259)(232,260)(233,253)(234,254)(235,255)(236,256)
(237,249)(238,250)(239,251)(240,252)(241,245)(242,246)(243,247)(244,248);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9, 41)( 10, 42)( 11, 44)( 12, 43)
( 13, 37)( 14, 38)( 15, 40)( 16, 39)( 17, 33)( 18, 34)( 19, 36)( 20, 35)
( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 27, 28)( 45, 93)( 46, 94)( 47, 96)
( 48, 95)( 49, 89)( 50, 90)( 51, 92)( 52, 91)( 53,129)( 54,130)( 55,132)
( 56,131)( 57,125)( 58,126)( 59,128)( 60,127)( 61,121)( 62,122)( 63,124)
( 64,123)( 65,117)( 66,118)( 67,120)( 68,119)( 69,113)( 70,114)( 71,116)
( 72,115)( 73,109)( 74,110)( 75,112)( 76,111)( 77,105)( 78,106)( 79,108)
( 80,107)( 81,101)( 82,102)( 83,104)( 84,103)( 85, 97)( 86, 98)( 87,100)
( 88, 99)(133,137)(134,138)(135,140)(136,139)(141,173)(142,174)(143,176)
(144,175)(145,169)(146,170)(147,172)(148,171)(149,165)(150,166)(151,168)
(152,167)(153,161)(154,162)(155,164)(156,163)(159,160)(177,225)(178,226)
(179,228)(180,227)(181,221)(182,222)(183,224)(184,223)(185,261)(186,262)
(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)(193,253)(194,254)
(195,256)(196,255)(197,249)(198,250)(199,252)(200,251)(201,245)(202,246)
(203,248)(204,247)(205,241)(206,242)(207,244)(208,243)(209,237)(210,238)
(211,240)(212,239)(213,233)(214,234)(215,236)(216,235)(217,229)(218,230)
(219,232)(220,231);;
s2 := ( 1,177)( 2,180)( 3,179)( 4,178)( 5,181)( 6,184)( 7,183)( 8,182)
( 9,185)( 10,188)( 11,187)( 12,186)( 13,189)( 14,192)( 15,191)( 16,190)
( 17,193)( 18,196)( 19,195)( 20,194)( 21,197)( 22,200)( 23,199)( 24,198)
( 25,201)( 26,204)( 27,203)( 28,202)( 29,205)( 30,208)( 31,207)( 32,206)
( 33,209)( 34,212)( 35,211)( 36,210)( 37,213)( 38,216)( 39,215)( 40,214)
( 41,217)( 42,220)( 43,219)( 44,218)( 45,133)( 46,136)( 47,135)( 48,134)
( 49,137)( 50,140)( 51,139)( 52,138)( 53,141)( 54,144)( 55,143)( 56,142)
( 57,145)( 58,148)( 59,147)( 60,146)( 61,149)( 62,152)( 63,151)( 64,150)
( 65,153)( 66,156)( 67,155)( 68,154)( 69,157)( 70,160)( 71,159)( 72,158)
( 73,161)( 74,164)( 75,163)( 76,162)( 77,165)( 78,168)( 79,167)( 80,166)
( 81,169)( 82,172)( 83,171)( 84,170)( 85,173)( 86,176)( 87,175)( 88,174)
( 89,221)( 90,224)( 91,223)( 92,222)( 93,225)( 94,228)( 95,227)( 96,226)
( 97,229)( 98,232)( 99,231)(100,230)(101,233)(102,236)(103,235)(104,234)
(105,237)(106,240)(107,239)(108,238)(109,241)(110,244)(111,243)(112,242)
(113,245)(114,248)(115,247)(116,246)(117,249)(118,252)(119,251)(120,250)
(121,253)(122,256)(123,255)(124,254)(125,257)(126,260)(127,259)(128,258)
(129,261)(130,264)(131,263)(132,262);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(264)!( 5, 41)( 6, 42)( 7, 43)( 8, 44)( 9, 37)( 10, 38)( 11, 39)
( 12, 40)( 13, 33)( 14, 34)( 15, 35)( 16, 36)( 17, 29)( 18, 30)( 19, 31)
( 20, 32)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 49, 85)( 50, 86)( 51, 87)
( 52, 88)( 53, 81)( 54, 82)( 55, 83)( 56, 84)( 57, 77)( 58, 78)( 59, 79)
( 60, 80)( 61, 73)( 62, 74)( 63, 75)( 64, 76)( 65, 69)( 66, 70)( 67, 71)
( 68, 72)( 93,129)( 94,130)( 95,131)( 96,132)( 97,125)( 98,126)( 99,127)
(100,128)(101,121)(102,122)(103,123)(104,124)(105,117)(106,118)(107,119)
(108,120)(109,113)(110,114)(111,115)(112,116)(137,173)(138,174)(139,175)
(140,176)(141,169)(142,170)(143,171)(144,172)(145,165)(146,166)(147,167)
(148,168)(149,161)(150,162)(151,163)(152,164)(153,157)(154,158)(155,159)
(156,160)(181,217)(182,218)(183,219)(184,220)(185,213)(186,214)(187,215)
(188,216)(189,209)(190,210)(191,211)(192,212)(193,205)(194,206)(195,207)
(196,208)(197,201)(198,202)(199,203)(200,204)(225,261)(226,262)(227,263)
(228,264)(229,257)(230,258)(231,259)(232,260)(233,253)(234,254)(235,255)
(236,256)(237,249)(238,250)(239,251)(240,252)(241,245)(242,246)(243,247)
(244,248);
s1 := Sym(264)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9, 41)( 10, 42)( 11, 44)
( 12, 43)( 13, 37)( 14, 38)( 15, 40)( 16, 39)( 17, 33)( 18, 34)( 19, 36)
( 20, 35)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 27, 28)( 45, 93)( 46, 94)
( 47, 96)( 48, 95)( 49, 89)( 50, 90)( 51, 92)( 52, 91)( 53,129)( 54,130)
( 55,132)( 56,131)( 57,125)( 58,126)( 59,128)( 60,127)( 61,121)( 62,122)
( 63,124)( 64,123)( 65,117)( 66,118)( 67,120)( 68,119)( 69,113)( 70,114)
( 71,116)( 72,115)( 73,109)( 74,110)( 75,112)( 76,111)( 77,105)( 78,106)
( 79,108)( 80,107)( 81,101)( 82,102)( 83,104)( 84,103)( 85, 97)( 86, 98)
( 87,100)( 88, 99)(133,137)(134,138)(135,140)(136,139)(141,173)(142,174)
(143,176)(144,175)(145,169)(146,170)(147,172)(148,171)(149,165)(150,166)
(151,168)(152,167)(153,161)(154,162)(155,164)(156,163)(159,160)(177,225)
(178,226)(179,228)(180,227)(181,221)(182,222)(183,224)(184,223)(185,261)
(186,262)(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)(193,253)
(194,254)(195,256)(196,255)(197,249)(198,250)(199,252)(200,251)(201,245)
(202,246)(203,248)(204,247)(205,241)(206,242)(207,244)(208,243)(209,237)
(210,238)(211,240)(212,239)(213,233)(214,234)(215,236)(216,235)(217,229)
(218,230)(219,232)(220,231);
s2 := Sym(264)!( 1,177)( 2,180)( 3,179)( 4,178)( 5,181)( 6,184)( 7,183)
( 8,182)( 9,185)( 10,188)( 11,187)( 12,186)( 13,189)( 14,192)( 15,191)
( 16,190)( 17,193)( 18,196)( 19,195)( 20,194)( 21,197)( 22,200)( 23,199)
( 24,198)( 25,201)( 26,204)( 27,203)( 28,202)( 29,205)( 30,208)( 31,207)
( 32,206)( 33,209)( 34,212)( 35,211)( 36,210)( 37,213)( 38,216)( 39,215)
( 40,214)( 41,217)( 42,220)( 43,219)( 44,218)( 45,133)( 46,136)( 47,135)
( 48,134)( 49,137)( 50,140)( 51,139)( 52,138)( 53,141)( 54,144)( 55,143)
( 56,142)( 57,145)( 58,148)( 59,147)( 60,146)( 61,149)( 62,152)( 63,151)
( 64,150)( 65,153)( 66,156)( 67,155)( 68,154)( 69,157)( 70,160)( 71,159)
( 72,158)( 73,161)( 74,164)( 75,163)( 76,162)( 77,165)( 78,168)( 79,167)
( 80,166)( 81,169)( 82,172)( 83,171)( 84,170)( 85,173)( 86,176)( 87,175)
( 88,174)( 89,221)( 90,224)( 91,223)( 92,222)( 93,225)( 94,228)( 95,227)
( 96,226)( 97,229)( 98,232)( 99,231)(100,230)(101,233)(102,236)(103,235)
(104,234)(105,237)(106,240)(107,239)(108,238)(109,241)(110,244)(111,243)
(112,242)(113,245)(114,248)(115,247)(116,246)(117,249)(118,252)(119,251)
(120,250)(121,253)(122,256)(123,255)(124,254)(125,257)(126,260)(127,259)
(128,258)(129,261)(130,264)(131,263)(132,262);
s3 := Sym(264)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264);
poly := sub<Sym(264)|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,
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope