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