Polytope of Type {12,10,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,10,2}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240399)
Rank : 4
Schlafli Type : {12,10,2}
Number of vertices, edges, etc : 48, 240, 40, 2
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
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) :
3-fold quotients : {4,10,2}*640b
6-fold quotients : {4,5,2}*320
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81,169)( 82,170)( 83,171)( 84,172)( 85,173)( 86,174)( 87,175)( 88,176)
( 89,161)( 90,162)( 91,163)( 92,164)( 93,165)( 94,166)( 95,167)( 96,168)
( 97,185)( 98,186)( 99,187)(100,188)(101,189)(102,190)(103,191)(104,192)
(105,177)(106,178)(107,179)(108,180)(109,181)(110,182)(111,183)(112,184)
(113,201)(114,202)(115,203)(116,204)(117,205)(118,206)(119,207)(120,208)
(121,193)(122,194)(123,195)(124,196)(125,197)(126,198)(127,199)(128,200)
(129,217)(130,218)(131,219)(132,220)(133,221)(134,222)(135,223)(136,224)
(137,209)(138,210)(139,211)(140,212)(141,213)(142,214)(143,215)(144,216)
(145,233)(146,234)(147,235)(148,236)(149,237)(150,238)(151,239)(152,240)
(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)(160,232);;
s1 := ( 1, 81)( 2, 91)( 3, 94)( 4, 88)( 5, 85)( 6, 95)( 7, 90)( 8, 84)
( 9, 93)( 10, 87)( 11, 82)( 12, 92)( 13, 89)( 14, 83)( 15, 86)( 16, 96)
( 17,145)( 18,155)( 19,158)( 20,152)( 21,149)( 22,159)( 23,154)( 24,148)
( 25,157)( 26,151)( 27,146)( 28,156)( 29,153)( 30,147)( 31,150)( 32,160)
( 33,129)( 34,139)( 35,142)( 36,136)( 37,133)( 38,143)( 39,138)( 40,132)
( 41,141)( 42,135)( 43,130)( 44,140)( 45,137)( 46,131)( 47,134)( 48,144)
( 49,113)( 50,123)( 51,126)( 52,120)( 53,117)( 54,127)( 55,122)( 56,116)
( 57,125)( 58,119)( 59,114)( 60,124)( 61,121)( 62,115)( 63,118)( 64,128)
( 65, 97)( 66,107)( 67,110)( 68,104)( 69,101)( 70,111)( 71,106)( 72,100)
( 73,109)( 74,103)( 75, 98)( 76,108)( 77,105)( 78, 99)( 79,102)( 80,112)
(162,171)(163,174)(164,168)(166,175)(167,170)(169,173)(177,225)(178,235)
(179,238)(180,232)(181,229)(182,239)(183,234)(184,228)(185,237)(186,231)
(187,226)(188,236)(189,233)(190,227)(191,230)(192,240)(193,209)(194,219)
(195,222)(196,216)(197,213)(198,223)(199,218)(200,212)(201,221)(202,215)
(203,210)(204,220)(205,217)(206,211)(207,214)(208,224);;
s2 := ( 1, 33)( 2, 45)( 3, 40)( 4, 44)( 5, 42)( 6, 38)( 7, 47)( 8, 35)
( 9, 41)( 10, 37)( 11, 48)( 12, 36)( 13, 34)( 14, 46)( 15, 39)( 16, 43)
( 18, 29)( 19, 24)( 20, 28)( 21, 26)( 23, 31)( 27, 32)( 49, 65)( 50, 77)
( 51, 72)( 52, 76)( 53, 74)( 54, 70)( 55, 79)( 56, 67)( 57, 73)( 58, 69)
( 59, 80)( 60, 68)( 61, 66)( 62, 78)( 63, 71)( 64, 75)( 81,113)( 82,125)
( 83,120)( 84,124)( 85,122)( 86,118)( 87,127)( 88,115)( 89,121)( 90,117)
( 91,128)( 92,116)( 93,114)( 94,126)( 95,119)( 96,123)( 98,109)( 99,104)
(100,108)(101,106)(103,111)(107,112)(129,145)(130,157)(131,152)(132,156)
(133,154)(134,150)(135,159)(136,147)(137,153)(138,149)(139,160)(140,148)
(141,146)(142,158)(143,151)(144,155)(161,193)(162,205)(163,200)(164,204)
(165,202)(166,198)(167,207)(168,195)(169,201)(170,197)(171,208)(172,196)
(173,194)(174,206)(175,199)(176,203)(178,189)(179,184)(180,188)(181,186)
(183,191)(187,192)(209,225)(210,237)(211,232)(212,236)(213,234)(214,230)
(215,239)(216,227)(217,233)(218,229)(219,240)(220,228)(221,226)(222,238)
(223,231)(224,235);;
s3 := (241,242);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(242)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81,169)( 82,170)( 83,171)( 84,172)( 85,173)( 86,174)( 87,175)
( 88,176)( 89,161)( 90,162)( 91,163)( 92,164)( 93,165)( 94,166)( 95,167)
( 96,168)( 97,185)( 98,186)( 99,187)(100,188)(101,189)(102,190)(103,191)
(104,192)(105,177)(106,178)(107,179)(108,180)(109,181)(110,182)(111,183)
(112,184)(113,201)(114,202)(115,203)(116,204)(117,205)(118,206)(119,207)
(120,208)(121,193)(122,194)(123,195)(124,196)(125,197)(126,198)(127,199)
(128,200)(129,217)(130,218)(131,219)(132,220)(133,221)(134,222)(135,223)
(136,224)(137,209)(138,210)(139,211)(140,212)(141,213)(142,214)(143,215)
(144,216)(145,233)(146,234)(147,235)(148,236)(149,237)(150,238)(151,239)
(152,240)(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)
(160,232);
s1 := Sym(242)!( 1, 81)( 2, 91)( 3, 94)( 4, 88)( 5, 85)( 6, 95)( 7, 90)
( 8, 84)( 9, 93)( 10, 87)( 11, 82)( 12, 92)( 13, 89)( 14, 83)( 15, 86)
( 16, 96)( 17,145)( 18,155)( 19,158)( 20,152)( 21,149)( 22,159)( 23,154)
( 24,148)( 25,157)( 26,151)( 27,146)( 28,156)( 29,153)( 30,147)( 31,150)
( 32,160)( 33,129)( 34,139)( 35,142)( 36,136)( 37,133)( 38,143)( 39,138)
( 40,132)( 41,141)( 42,135)( 43,130)( 44,140)( 45,137)( 46,131)( 47,134)
( 48,144)( 49,113)( 50,123)( 51,126)( 52,120)( 53,117)( 54,127)( 55,122)
( 56,116)( 57,125)( 58,119)( 59,114)( 60,124)( 61,121)( 62,115)( 63,118)
( 64,128)( 65, 97)( 66,107)( 67,110)( 68,104)( 69,101)( 70,111)( 71,106)
( 72,100)( 73,109)( 74,103)( 75, 98)( 76,108)( 77,105)( 78, 99)( 79,102)
( 80,112)(162,171)(163,174)(164,168)(166,175)(167,170)(169,173)(177,225)
(178,235)(179,238)(180,232)(181,229)(182,239)(183,234)(184,228)(185,237)
(186,231)(187,226)(188,236)(189,233)(190,227)(191,230)(192,240)(193,209)
(194,219)(195,222)(196,216)(197,213)(198,223)(199,218)(200,212)(201,221)
(202,215)(203,210)(204,220)(205,217)(206,211)(207,214)(208,224);
s2 := Sym(242)!( 1, 33)( 2, 45)( 3, 40)( 4, 44)( 5, 42)( 6, 38)( 7, 47)
( 8, 35)( 9, 41)( 10, 37)( 11, 48)( 12, 36)( 13, 34)( 14, 46)( 15, 39)
( 16, 43)( 18, 29)( 19, 24)( 20, 28)( 21, 26)( 23, 31)( 27, 32)( 49, 65)
( 50, 77)( 51, 72)( 52, 76)( 53, 74)( 54, 70)( 55, 79)( 56, 67)( 57, 73)
( 58, 69)( 59, 80)( 60, 68)( 61, 66)( 62, 78)( 63, 71)( 64, 75)( 81,113)
( 82,125)( 83,120)( 84,124)( 85,122)( 86,118)( 87,127)( 88,115)( 89,121)
( 90,117)( 91,128)( 92,116)( 93,114)( 94,126)( 95,119)( 96,123)( 98,109)
( 99,104)(100,108)(101,106)(103,111)(107,112)(129,145)(130,157)(131,152)
(132,156)(133,154)(134,150)(135,159)(136,147)(137,153)(138,149)(139,160)
(140,148)(141,146)(142,158)(143,151)(144,155)(161,193)(162,205)(163,200)
(164,204)(165,202)(166,198)(167,207)(168,195)(169,201)(170,197)(171,208)
(172,196)(173,194)(174,206)(175,199)(176,203)(178,189)(179,184)(180,188)
(181,186)(183,191)(187,192)(209,225)(210,237)(211,232)(212,236)(213,234)
(214,230)(215,239)(216,227)(217,233)(218,229)(219,240)(220,228)(221,226)
(222,238)(223,231)(224,235);
s3 := Sym(242)!(241,242);
poly := sub<Sym(242)|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,
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope