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