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