Polytope of Type {2,3,8,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,8,10}*1920
if this polytope has a name.
Group : SmallGroup(1920,240195)
Rank : 5
Schlafli Type : {2,3,8,10}
Number of vertices, edges, etc : 2, 6, 24, 80, 10
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 : {2,3,4,10}*960
5-fold quotients : {2,3,8,2}*384
8-fold quotients : {2,3,2,10}*240
10-fold quotients : {2,3,4,2}*192
16-fold quotients : {2,3,2,5}*120
20-fold quotients : {2,3,4,2}*96
40-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 8)( 6, 7)( 9, 10)( 13, 16)( 14, 15)( 17, 18)( 21, 24)( 22, 23)
( 25, 26)( 29, 32)( 30, 31)( 33, 34)( 37, 40)( 38, 39)( 41, 42)( 43, 83)
( 44, 84)( 45, 88)( 46, 87)( 47, 86)( 48, 85)( 49, 90)( 50, 89)( 51, 91)
( 52, 92)( 53, 96)( 54, 95)( 55, 94)( 56, 93)( 57, 98)( 58, 97)( 59, 99)
( 60,100)( 61,104)( 62,103)( 63,102)( 64,101)( 65,106)( 66,105)( 67,107)
( 68,108)( 69,112)( 70,111)( 71,110)( 72,109)( 73,114)( 74,113)( 75,115)
( 76,116)( 77,120)( 78,119)( 79,118)( 80,117)( 81,122)( 82,121)(123,124)
(125,127)(126,128)(131,132)(133,135)(134,136)(139,140)(141,143)(142,144)
(147,148)(149,151)(150,152)(155,156)(157,159)(158,160)(163,204)(164,203)
(165,207)(166,208)(167,205)(168,206)(169,209)(170,210)(171,212)(172,211)
(173,215)(174,216)(175,213)(176,214)(177,217)(178,218)(179,220)(180,219)
(181,223)(182,224)(183,221)(184,222)(185,225)(186,226)(187,228)(188,227)
(189,231)(190,232)(191,229)(192,230)(193,233)(194,234)(195,236)(196,235)
(197,239)(198,240)(199,237)(200,238)(201,241)(202,242);;
s2 := ( 3, 43)( 4, 44)( 5, 46)( 6, 45)( 7, 49)( 8, 50)( 9, 47)( 10, 48)
( 11, 51)( 12, 52)( 13, 54)( 14, 53)( 15, 57)( 16, 58)( 17, 55)( 18, 56)
( 19, 59)( 20, 60)( 21, 62)( 22, 61)( 23, 65)( 24, 66)( 25, 63)( 26, 64)
( 27, 67)( 28, 68)( 29, 70)( 30, 69)( 31, 73)( 32, 74)( 33, 71)( 34, 72)
( 35, 75)( 36, 76)( 37, 78)( 38, 77)( 39, 81)( 40, 82)( 41, 79)( 42, 80)
( 85, 86)( 87, 89)( 88, 90)( 93, 94)( 95, 97)( 96, 98)(101,102)(103,105)
(104,106)(109,110)(111,113)(112,114)(117,118)(119,121)(120,122)(123,164)
(124,163)(125,165)(126,166)(127,170)(128,169)(129,168)(130,167)(131,172)
(132,171)(133,173)(134,174)(135,178)(136,177)(137,176)(138,175)(139,180)
(140,179)(141,181)(142,182)(143,186)(144,185)(145,184)(146,183)(147,188)
(148,187)(149,189)(150,190)(151,194)(152,193)(153,192)(154,191)(155,196)
(156,195)(157,197)(158,198)(159,202)(160,201)(161,200)(162,199)(203,204)
(207,210)(208,209)(211,212)(215,218)(216,217)(219,220)(223,226)(224,225)
(227,228)(231,234)(232,233)(235,236)(239,242)(240,241);;
s3 := ( 3,129)( 4,130)( 5,127)( 6,128)( 7,126)( 8,125)( 9,124)( 10,123)
( 11,161)( 12,162)( 13,159)( 14,160)( 15,158)( 16,157)( 17,156)( 18,155)
( 19,153)( 20,154)( 21,151)( 22,152)( 23,150)( 24,149)( 25,148)( 26,147)
( 27,145)( 28,146)( 29,143)( 30,144)( 31,142)( 32,141)( 33,140)( 34,139)
( 35,137)( 36,138)( 37,135)( 38,136)( 39,134)( 40,133)( 41,132)( 42,131)
( 43,169)( 44,170)( 45,167)( 46,168)( 47,166)( 48,165)( 49,164)( 50,163)
( 51,201)( 52,202)( 53,199)( 54,200)( 55,198)( 56,197)( 57,196)( 58,195)
( 59,193)( 60,194)( 61,191)( 62,192)( 63,190)( 64,189)( 65,188)( 66,187)
( 67,185)( 68,186)( 69,183)( 70,184)( 71,182)( 72,181)( 73,180)( 74,179)
( 75,177)( 76,178)( 77,175)( 78,176)( 79,174)( 80,173)( 81,172)( 82,171)
( 83,209)( 84,210)( 85,207)( 86,208)( 87,206)( 88,205)( 89,204)( 90,203)
( 91,241)( 92,242)( 93,239)( 94,240)( 95,238)( 96,237)( 97,236)( 98,235)
( 99,233)(100,234)(101,231)(102,232)(103,230)(104,229)(105,228)(106,227)
(107,225)(108,226)(109,223)(110,224)(111,222)(112,221)(113,220)(114,219)
(115,217)(116,218)(117,215)(118,216)(119,214)(120,213)(121,212)(122,211);;
s4 := ( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)( 10, 18)
( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 39)( 24, 40)( 25, 41)( 26, 42)
( 43, 51)( 44, 52)( 45, 53)( 46, 54)( 47, 55)( 48, 56)( 49, 57)( 50, 58)
( 59, 75)( 60, 76)( 61, 77)( 62, 78)( 63, 79)( 64, 80)( 65, 81)( 66, 82)
( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)( 90, 98)
( 99,115)(100,116)(101,117)(102,118)(103,119)(104,120)(105,121)(106,122)
(123,131)(124,132)(125,133)(126,134)(127,135)(128,136)(129,137)(130,138)
(139,155)(140,156)(141,157)(142,158)(143,159)(144,160)(145,161)(146,162)
(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(169,177)(170,178)
(179,195)(180,196)(181,197)(182,198)(183,199)(184,200)(185,201)(186,202)
(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)(209,217)(210,218)
(219,235)(220,236)(221,237)(222,238)(223,239)(224,240)(225,241)(226,242);;
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, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2,
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(242)!(1,2);
s1 := Sym(242)!( 5, 8)( 6, 7)( 9, 10)( 13, 16)( 14, 15)( 17, 18)( 21, 24)
( 22, 23)( 25, 26)( 29, 32)( 30, 31)( 33, 34)( 37, 40)( 38, 39)( 41, 42)
( 43, 83)( 44, 84)( 45, 88)( 46, 87)( 47, 86)( 48, 85)( 49, 90)( 50, 89)
( 51, 91)( 52, 92)( 53, 96)( 54, 95)( 55, 94)( 56, 93)( 57, 98)( 58, 97)
( 59, 99)( 60,100)( 61,104)( 62,103)( 63,102)( 64,101)( 65,106)( 66,105)
( 67,107)( 68,108)( 69,112)( 70,111)( 71,110)( 72,109)( 73,114)( 74,113)
( 75,115)( 76,116)( 77,120)( 78,119)( 79,118)( 80,117)( 81,122)( 82,121)
(123,124)(125,127)(126,128)(131,132)(133,135)(134,136)(139,140)(141,143)
(142,144)(147,148)(149,151)(150,152)(155,156)(157,159)(158,160)(163,204)
(164,203)(165,207)(166,208)(167,205)(168,206)(169,209)(170,210)(171,212)
(172,211)(173,215)(174,216)(175,213)(176,214)(177,217)(178,218)(179,220)
(180,219)(181,223)(182,224)(183,221)(184,222)(185,225)(186,226)(187,228)
(188,227)(189,231)(190,232)(191,229)(192,230)(193,233)(194,234)(195,236)
(196,235)(197,239)(198,240)(199,237)(200,238)(201,241)(202,242);
s2 := Sym(242)!( 3, 43)( 4, 44)( 5, 46)( 6, 45)( 7, 49)( 8, 50)( 9, 47)
( 10, 48)( 11, 51)( 12, 52)( 13, 54)( 14, 53)( 15, 57)( 16, 58)( 17, 55)
( 18, 56)( 19, 59)( 20, 60)( 21, 62)( 22, 61)( 23, 65)( 24, 66)( 25, 63)
( 26, 64)( 27, 67)( 28, 68)( 29, 70)( 30, 69)( 31, 73)( 32, 74)( 33, 71)
( 34, 72)( 35, 75)( 36, 76)( 37, 78)( 38, 77)( 39, 81)( 40, 82)( 41, 79)
( 42, 80)( 85, 86)( 87, 89)( 88, 90)( 93, 94)( 95, 97)( 96, 98)(101,102)
(103,105)(104,106)(109,110)(111,113)(112,114)(117,118)(119,121)(120,122)
(123,164)(124,163)(125,165)(126,166)(127,170)(128,169)(129,168)(130,167)
(131,172)(132,171)(133,173)(134,174)(135,178)(136,177)(137,176)(138,175)
(139,180)(140,179)(141,181)(142,182)(143,186)(144,185)(145,184)(146,183)
(147,188)(148,187)(149,189)(150,190)(151,194)(152,193)(153,192)(154,191)
(155,196)(156,195)(157,197)(158,198)(159,202)(160,201)(161,200)(162,199)
(203,204)(207,210)(208,209)(211,212)(215,218)(216,217)(219,220)(223,226)
(224,225)(227,228)(231,234)(232,233)(235,236)(239,242)(240,241);
s3 := Sym(242)!( 3,129)( 4,130)( 5,127)( 6,128)( 7,126)( 8,125)( 9,124)
( 10,123)( 11,161)( 12,162)( 13,159)( 14,160)( 15,158)( 16,157)( 17,156)
( 18,155)( 19,153)( 20,154)( 21,151)( 22,152)( 23,150)( 24,149)( 25,148)
( 26,147)( 27,145)( 28,146)( 29,143)( 30,144)( 31,142)( 32,141)( 33,140)
( 34,139)( 35,137)( 36,138)( 37,135)( 38,136)( 39,134)( 40,133)( 41,132)
( 42,131)( 43,169)( 44,170)( 45,167)( 46,168)( 47,166)( 48,165)( 49,164)
( 50,163)( 51,201)( 52,202)( 53,199)( 54,200)( 55,198)( 56,197)( 57,196)
( 58,195)( 59,193)( 60,194)( 61,191)( 62,192)( 63,190)( 64,189)( 65,188)
( 66,187)( 67,185)( 68,186)( 69,183)( 70,184)( 71,182)( 72,181)( 73,180)
( 74,179)( 75,177)( 76,178)( 77,175)( 78,176)( 79,174)( 80,173)( 81,172)
( 82,171)( 83,209)( 84,210)( 85,207)( 86,208)( 87,206)( 88,205)( 89,204)
( 90,203)( 91,241)( 92,242)( 93,239)( 94,240)( 95,238)( 96,237)( 97,236)
( 98,235)( 99,233)(100,234)(101,231)(102,232)(103,230)(104,229)(105,228)
(106,227)(107,225)(108,226)(109,223)(110,224)(111,222)(112,221)(113,220)
(114,219)(115,217)(116,218)(117,215)(118,216)(119,214)(120,213)(121,212)
(122,211);
s4 := Sym(242)!( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)
( 10, 18)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 39)( 24, 40)( 25, 41)
( 26, 42)( 43, 51)( 44, 52)( 45, 53)( 46, 54)( 47, 55)( 48, 56)( 49, 57)
( 50, 58)( 59, 75)( 60, 76)( 61, 77)( 62, 78)( 63, 79)( 64, 80)( 65, 81)
( 66, 82)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)
( 90, 98)( 99,115)(100,116)(101,117)(102,118)(103,119)(104,120)(105,121)
(106,122)(123,131)(124,132)(125,133)(126,134)(127,135)(128,136)(129,137)
(130,138)(139,155)(140,156)(141,157)(142,158)(143,159)(144,160)(145,161)
(146,162)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(169,177)
(170,178)(179,195)(180,196)(181,197)(182,198)(183,199)(184,200)(185,201)
(186,202)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)(209,217)
(210,218)(219,235)(220,236)(221,237)(222,238)(223,239)(224,240)(225,241)
(226,242);
poly := sub<Sym(242)|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,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope