Polytope of Type {2,2,15,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,15,8}*1920
if this polytope has a name.
Group : SmallGroup(1920,240302)
Rank : 5
Schlafli Type : {2,2,15,8}
Number of vertices, edges, etc : 2, 2, 30, 120, 16
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 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) :
2-fold quotients : {2,2,15,4}*960
4-fold quotients : {2,2,15,4}*480
5-fold quotients : {2,2,3,8}*384
8-fold quotients : {2,2,15,2}*240
10-fold quotients : {2,2,3,4}*192
20-fold quotients : {2,2,3,4}*96
24-fold quotients : {2,2,5,2}*80
40-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 7, 9)( 8, 10)( 11, 12)( 13, 37)( 14, 38)( 15, 41)( 16, 42)( 17, 39)
( 18, 40)( 19, 44)( 20, 43)( 21, 29)( 22, 30)( 23, 33)( 24, 34)( 25, 31)
( 26, 32)( 27, 36)( 28, 35)( 45, 85)( 46, 86)( 47, 89)( 48, 90)( 49, 87)
( 50, 88)( 51, 92)( 52, 91)( 53,117)( 54,118)( 55,121)( 56,122)( 57,119)
( 58,120)( 59,124)( 60,123)( 61,109)( 62,110)( 63,113)( 64,114)( 65,111)
( 66,112)( 67,116)( 68,115)( 69,101)( 70,102)( 71,105)( 72,106)( 73,103)
( 74,104)( 75,108)( 76,107)( 77, 93)( 78, 94)( 79, 97)( 80, 98)( 81, 95)
( 82, 96)( 83,100)( 84, 99)(125,126)(127,130)(128,129)(133,158)(134,157)
(135,162)(136,161)(137,160)(138,159)(139,163)(140,164)(141,150)(142,149)
(143,154)(144,153)(145,152)(146,151)(147,155)(148,156)(165,206)(166,205)
(167,210)(168,209)(169,208)(170,207)(171,211)(172,212)(173,238)(174,237)
(175,242)(176,241)(177,240)(178,239)(179,243)(180,244)(181,230)(182,229)
(183,234)(184,233)(185,232)(186,231)(187,235)(188,236)(189,222)(190,221)
(191,226)(192,225)(193,224)(194,223)(195,227)(196,228)(197,214)(198,213)
(199,218)(200,217)(201,216)(202,215)(203,219)(204,220);;
s3 := ( 5, 53)( 6, 54)( 7, 56)( 8, 55)( 9, 59)( 10, 60)( 11, 57)( 12, 58)
( 13, 45)( 14, 46)( 15, 48)( 16, 47)( 17, 51)( 18, 52)( 19, 49)( 20, 50)
( 21, 77)( 22, 78)( 23, 80)( 24, 79)( 25, 83)( 26, 84)( 27, 81)( 28, 82)
( 29, 69)( 30, 70)( 31, 72)( 32, 71)( 33, 75)( 34, 76)( 35, 73)( 36, 74)
( 37, 61)( 38, 62)( 39, 64)( 40, 63)( 41, 67)( 42, 68)( 43, 65)( 44, 66)
( 85, 93)( 86, 94)( 87, 96)( 88, 95)( 89, 99)( 90,100)( 91, 97)( 92, 98)
(101,117)(102,118)(103,120)(104,119)(105,123)(106,124)(107,121)(108,122)
(111,112)(113,115)(114,116)(125,174)(126,173)(127,175)(128,176)(129,180)
(130,179)(131,178)(132,177)(133,166)(134,165)(135,167)(136,168)(137,172)
(138,171)(139,170)(140,169)(141,198)(142,197)(143,199)(144,200)(145,204)
(146,203)(147,202)(148,201)(149,190)(150,189)(151,191)(152,192)(153,196)
(154,195)(155,194)(156,193)(157,182)(158,181)(159,183)(160,184)(161,188)
(162,187)(163,186)(164,185)(205,214)(206,213)(207,215)(208,216)(209,220)
(210,219)(211,218)(212,217)(221,238)(222,237)(223,239)(224,240)(225,244)
(226,243)(227,242)(228,241)(229,230)(233,236)(234,235);;
s4 := ( 5,131)( 6,132)( 7,129)( 8,130)( 9,128)( 10,127)( 11,126)( 12,125)
( 13,139)( 14,140)( 15,137)( 16,138)( 17,136)( 18,135)( 19,134)( 20,133)
( 21,147)( 22,148)( 23,145)( 24,146)( 25,144)( 26,143)( 27,142)( 28,141)
( 29,155)( 30,156)( 31,153)( 32,154)( 33,152)( 34,151)( 35,150)( 36,149)
( 37,163)( 38,164)( 39,161)( 40,162)( 41,160)( 42,159)( 43,158)( 44,157)
( 45,171)( 46,172)( 47,169)( 48,170)( 49,168)( 50,167)( 51,166)( 52,165)
( 53,179)( 54,180)( 55,177)( 56,178)( 57,176)( 58,175)( 59,174)( 60,173)
( 61,187)( 62,188)( 63,185)( 64,186)( 65,184)( 66,183)( 67,182)( 68,181)
( 69,195)( 70,196)( 71,193)( 72,194)( 73,192)( 74,191)( 75,190)( 76,189)
( 77,203)( 78,204)( 79,201)( 80,202)( 81,200)( 82,199)( 83,198)( 84,197)
( 85,211)( 86,212)( 87,209)( 88,210)( 89,208)( 90,207)( 91,206)( 92,205)
( 93,219)( 94,220)( 95,217)( 96,218)( 97,216)( 98,215)( 99,214)(100,213)
(101,227)(102,228)(103,225)(104,226)(105,224)(106,223)(107,222)(108,221)
(109,235)(110,236)(111,233)(112,234)(113,232)(114,231)(115,230)(116,229)
(117,243)(118,244)(119,241)(120,242)(121,240)(122,239)(123,238)(124,237);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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(244)!(1,2);
s1 := Sym(244)!(3,4);
s2 := Sym(244)!( 7, 9)( 8, 10)( 11, 12)( 13, 37)( 14, 38)( 15, 41)( 16, 42)
( 17, 39)( 18, 40)( 19, 44)( 20, 43)( 21, 29)( 22, 30)( 23, 33)( 24, 34)
( 25, 31)( 26, 32)( 27, 36)( 28, 35)( 45, 85)( 46, 86)( 47, 89)( 48, 90)
( 49, 87)( 50, 88)( 51, 92)( 52, 91)( 53,117)( 54,118)( 55,121)( 56,122)
( 57,119)( 58,120)( 59,124)( 60,123)( 61,109)( 62,110)( 63,113)( 64,114)
( 65,111)( 66,112)( 67,116)( 68,115)( 69,101)( 70,102)( 71,105)( 72,106)
( 73,103)( 74,104)( 75,108)( 76,107)( 77, 93)( 78, 94)( 79, 97)( 80, 98)
( 81, 95)( 82, 96)( 83,100)( 84, 99)(125,126)(127,130)(128,129)(133,158)
(134,157)(135,162)(136,161)(137,160)(138,159)(139,163)(140,164)(141,150)
(142,149)(143,154)(144,153)(145,152)(146,151)(147,155)(148,156)(165,206)
(166,205)(167,210)(168,209)(169,208)(170,207)(171,211)(172,212)(173,238)
(174,237)(175,242)(176,241)(177,240)(178,239)(179,243)(180,244)(181,230)
(182,229)(183,234)(184,233)(185,232)(186,231)(187,235)(188,236)(189,222)
(190,221)(191,226)(192,225)(193,224)(194,223)(195,227)(196,228)(197,214)
(198,213)(199,218)(200,217)(201,216)(202,215)(203,219)(204,220);
s3 := Sym(244)!( 5, 53)( 6, 54)( 7, 56)( 8, 55)( 9, 59)( 10, 60)( 11, 57)
( 12, 58)( 13, 45)( 14, 46)( 15, 48)( 16, 47)( 17, 51)( 18, 52)( 19, 49)
( 20, 50)( 21, 77)( 22, 78)( 23, 80)( 24, 79)( 25, 83)( 26, 84)( 27, 81)
( 28, 82)( 29, 69)( 30, 70)( 31, 72)( 32, 71)( 33, 75)( 34, 76)( 35, 73)
( 36, 74)( 37, 61)( 38, 62)( 39, 64)( 40, 63)( 41, 67)( 42, 68)( 43, 65)
( 44, 66)( 85, 93)( 86, 94)( 87, 96)( 88, 95)( 89, 99)( 90,100)( 91, 97)
( 92, 98)(101,117)(102,118)(103,120)(104,119)(105,123)(106,124)(107,121)
(108,122)(111,112)(113,115)(114,116)(125,174)(126,173)(127,175)(128,176)
(129,180)(130,179)(131,178)(132,177)(133,166)(134,165)(135,167)(136,168)
(137,172)(138,171)(139,170)(140,169)(141,198)(142,197)(143,199)(144,200)
(145,204)(146,203)(147,202)(148,201)(149,190)(150,189)(151,191)(152,192)
(153,196)(154,195)(155,194)(156,193)(157,182)(158,181)(159,183)(160,184)
(161,188)(162,187)(163,186)(164,185)(205,214)(206,213)(207,215)(208,216)
(209,220)(210,219)(211,218)(212,217)(221,238)(222,237)(223,239)(224,240)
(225,244)(226,243)(227,242)(228,241)(229,230)(233,236)(234,235);
s4 := Sym(244)!( 5,131)( 6,132)( 7,129)( 8,130)( 9,128)( 10,127)( 11,126)
( 12,125)( 13,139)( 14,140)( 15,137)( 16,138)( 17,136)( 18,135)( 19,134)
( 20,133)( 21,147)( 22,148)( 23,145)( 24,146)( 25,144)( 26,143)( 27,142)
( 28,141)( 29,155)( 30,156)( 31,153)( 32,154)( 33,152)( 34,151)( 35,150)
( 36,149)( 37,163)( 38,164)( 39,161)( 40,162)( 41,160)( 42,159)( 43,158)
( 44,157)( 45,171)( 46,172)( 47,169)( 48,170)( 49,168)( 50,167)( 51,166)
( 52,165)( 53,179)( 54,180)( 55,177)( 56,178)( 57,176)( 58,175)( 59,174)
( 60,173)( 61,187)( 62,188)( 63,185)( 64,186)( 65,184)( 66,183)( 67,182)
( 68,181)( 69,195)( 70,196)( 71,193)( 72,194)( 73,192)( 74,191)( 75,190)
( 76,189)( 77,203)( 78,204)( 79,201)( 80,202)( 81,200)( 82,199)( 83,198)
( 84,197)( 85,211)( 86,212)( 87,209)( 88,210)( 89,208)( 90,207)( 91,206)
( 92,205)( 93,219)( 94,220)( 95,217)( 96,218)( 97,216)( 98,215)( 99,214)
(100,213)(101,227)(102,228)(103,225)(104,226)(105,224)(106,223)(107,222)
(108,221)(109,235)(110,236)(111,233)(112,234)(113,232)(114,231)(115,230)
(116,229)(117,243)(118,244)(119,241)(120,242)(121,240)(122,239)(123,238)
(124,237);
poly := sub<Sym(244)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope