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