Polytope of Type {2,10,15}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,15}*1920
if this polytope has a name.
Group : SmallGroup(1920,240399)
Rank : 4
Schlafli Type : {2,10,15}
Number of vertices, edges, etc : 2, 32, 240, 48
Order of s0s1s2s3 : 12
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) :
3-fold quotients : {2,10,5}*640b
6-fold quotients : {2,5,5}*320
80-fold quotients : {2,2,3}*24
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, 97)( 5, 92)( 6, 86)( 7, 83)( 8, 93)( 9, 96)( 10, 90)
( 11, 91)( 12, 85)( 13, 88)( 14, 98)( 15, 95)( 16, 89)( 17, 84)( 18, 94)
( 19,151)( 20,161)( 21,156)( 22,150)( 23,147)( 24,157)( 25,160)( 26,154)
( 27,155)( 28,149)( 29,152)( 30,162)( 31,159)( 32,153)( 33,148)( 34,158)
( 35,135)( 36,145)( 37,140)( 38,134)( 39,131)( 40,141)( 41,144)( 42,138)
( 43,139)( 44,133)( 45,136)( 46,146)( 47,143)( 48,137)( 49,132)( 50,142)
( 51,119)( 52,129)( 53,124)( 54,118)( 55,115)( 56,125)( 57,128)( 58,122)
( 59,123)( 60,117)( 61,120)( 62,130)( 63,127)( 64,121)( 65,116)( 66,126)
( 67,103)( 68,113)( 69,108)( 70,102)( 71, 99)( 72,109)( 73,112)( 74,106)
( 75,107)( 76,101)( 77,104)( 78,114)( 79,111)( 80,105)( 81,100)( 82,110)
(163,167)(164,177)(165,172)(168,173)(169,176)(174,178)(179,231)(180,241)
(181,236)(182,230)(183,227)(184,237)(185,240)(186,234)(187,235)(188,229)
(189,232)(190,242)(191,239)(192,233)(193,228)(194,238)(195,215)(196,225)
(197,220)(198,214)(199,211)(200,221)(201,224)(202,218)(203,219)(204,213)
(205,216)(206,226)(207,223)(208,217)(209,212)(210,222);;
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*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s1*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,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s3*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s3*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, 97)( 5, 92)( 6, 86)( 7, 83)( 8, 93)( 9, 96)
( 10, 90)( 11, 91)( 12, 85)( 13, 88)( 14, 98)( 15, 95)( 16, 89)( 17, 84)
( 18, 94)( 19,151)( 20,161)( 21,156)( 22,150)( 23,147)( 24,157)( 25,160)
( 26,154)( 27,155)( 28,149)( 29,152)( 30,162)( 31,159)( 32,153)( 33,148)
( 34,158)( 35,135)( 36,145)( 37,140)( 38,134)( 39,131)( 40,141)( 41,144)
( 42,138)( 43,139)( 44,133)( 45,136)( 46,146)( 47,143)( 48,137)( 49,132)
( 50,142)( 51,119)( 52,129)( 53,124)( 54,118)( 55,115)( 56,125)( 57,128)
( 58,122)( 59,123)( 60,117)( 61,120)( 62,130)( 63,127)( 64,121)( 65,116)
( 66,126)( 67,103)( 68,113)( 69,108)( 70,102)( 71, 99)( 72,109)( 73,112)
( 74,106)( 75,107)( 76,101)( 77,104)( 78,114)( 79,111)( 80,105)( 81,100)
( 82,110)(163,167)(164,177)(165,172)(168,173)(169,176)(174,178)(179,231)
(180,241)(181,236)(182,230)(183,227)(184,237)(185,240)(186,234)(187,235)
(188,229)(189,232)(190,242)(191,239)(192,233)(193,228)(194,238)(195,215)
(196,225)(197,220)(198,214)(199,211)(200,221)(201,224)(202,218)(203,219)
(204,213)(205,216)(206,226)(207,223)(208,217)(209,212)(210,222);
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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s1*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,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s3*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2 >;
to this polytope