Polytope of Type {10,8,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8,3}*960
if this polytope has a name.
Group : SmallGroup(960,10979)
Rank : 4
Schlafli Type : {10,8,3}
Number of vertices, edges, etc : 10, 80, 24, 6
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{10,8,3,2} of size 1920
Vertex Figure Of :
{2,10,8,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,4,3}*480
5-fold quotients : {2,8,3}*192
8-fold quotients : {10,2,3}*120
10-fold quotients : {2,4,3}*96
16-fold quotients : {5,2,3}*60
20-fold quotients : {2,4,3}*48
40-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,8,3}*1920, {10,8,6}*1920a
Permutation Representation (GAP) :
s0 := ( 9, 33)( 10, 34)( 11, 35)( 12, 36)( 13, 37)( 14, 38)( 15, 39)( 16, 40)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 49, 73)( 50, 74)( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)( 56, 80)
( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)
( 89,113)( 90,114)( 91,115)( 92,116)( 93,117)( 94,118)( 95,119)( 96,120)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(129,153)(130,154)(131,155)(132,156)(133,157)(134,158)(135,159)(136,160)
(137,145)(138,146)(139,147)(140,148)(141,149)(142,150)(143,151)(144,152)
(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)(176,200)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(209,233)(210,234)(211,235)(212,236)(213,237)(214,238)(215,239)(216,240)
(217,225)(218,226)(219,227)(220,228)(221,229)(222,230)(223,231)(224,232);;
s1 := ( 1,133)( 2,134)( 3,136)( 4,135)( 5,130)( 6,129)( 7,131)( 8,132)
( 9,125)( 10,126)( 11,128)( 12,127)( 13,122)( 14,121)( 15,123)( 16,124)
( 17,157)( 18,158)( 19,160)( 20,159)( 21,154)( 22,153)( 23,155)( 24,156)
( 25,149)( 26,150)( 27,152)( 28,151)( 29,146)( 30,145)( 31,147)( 32,148)
( 33,141)( 34,142)( 35,144)( 36,143)( 37,138)( 38,137)( 39,139)( 40,140)
( 41,173)( 42,174)( 43,176)( 44,175)( 45,170)( 46,169)( 47,171)( 48,172)
( 49,165)( 50,166)( 51,168)( 52,167)( 53,162)( 54,161)( 55,163)( 56,164)
( 57,197)( 58,198)( 59,200)( 60,199)( 61,194)( 62,193)( 63,195)( 64,196)
( 65,189)( 66,190)( 67,192)( 68,191)( 69,186)( 70,185)( 71,187)( 72,188)
( 73,181)( 74,182)( 75,184)( 76,183)( 77,178)( 78,177)( 79,179)( 80,180)
( 81,213)( 82,214)( 83,216)( 84,215)( 85,210)( 86,209)( 87,211)( 88,212)
( 89,205)( 90,206)( 91,208)( 92,207)( 93,202)( 94,201)( 95,203)( 96,204)
( 97,237)( 98,238)( 99,240)(100,239)(101,234)(102,233)(103,235)(104,236)
(105,229)(106,230)(107,232)(108,231)(109,226)(110,225)(111,227)(112,228)
(113,221)(114,222)(115,224)(116,223)(117,218)(118,217)(119,219)(120,220);;
s2 := ( 3, 6)( 4, 5)( 7, 8)( 11, 14)( 12, 13)( 15, 16)( 19, 22)( 20, 21)
( 23, 24)( 27, 30)( 28, 29)( 31, 32)( 35, 38)( 36, 37)( 39, 40)( 41, 81)
( 42, 82)( 43, 86)( 44, 85)( 45, 84)( 46, 83)( 47, 88)( 48, 87)( 49, 89)
( 50, 90)( 51, 94)( 52, 93)( 53, 92)( 54, 91)( 55, 96)( 56, 95)( 57, 97)
( 58, 98)( 59,102)( 60,101)( 61,100)( 62, 99)( 63,104)( 64,103)( 65,105)
( 66,106)( 67,110)( 68,109)( 69,108)( 70,107)( 71,112)( 72,111)( 73,113)
( 74,114)( 75,118)( 76,117)( 77,116)( 78,115)( 79,120)( 80,119)(121,122)
(123,125)(124,126)(129,130)(131,133)(132,134)(137,138)(139,141)(140,142)
(145,146)(147,149)(148,150)(153,154)(155,157)(156,158)(161,202)(162,201)
(163,205)(164,206)(165,203)(166,204)(167,207)(168,208)(169,210)(170,209)
(171,213)(172,214)(173,211)(174,212)(175,215)(176,216)(177,218)(178,217)
(179,221)(180,222)(181,219)(182,220)(183,223)(184,224)(185,226)(186,225)
(187,229)(188,230)(189,227)(190,228)(191,231)(192,232)(193,234)(194,233)
(195,237)(196,238)(197,235)(198,236)(199,239)(200,240);;
s3 := ( 1, 81)( 2, 82)( 3, 87)( 4, 88)( 5, 86)( 6, 85)( 7, 83)( 8, 84)
( 9, 89)( 10, 90)( 11, 95)( 12, 96)( 13, 94)( 14, 93)( 15, 91)( 16, 92)
( 17, 97)( 18, 98)( 19,103)( 20,104)( 21,102)( 22,101)( 23, 99)( 24,100)
( 25,105)( 26,106)( 27,111)( 28,112)( 29,110)( 30,109)( 31,107)( 32,108)
( 33,113)( 34,114)( 35,119)( 36,120)( 37,118)( 38,117)( 39,115)( 40,116)
( 43, 47)( 44, 48)( 45, 46)( 51, 55)( 52, 56)( 53, 54)( 59, 63)( 60, 64)
( 61, 62)( 67, 71)( 68, 72)( 69, 70)( 75, 79)( 76, 80)( 77, 78)(121,202)
(122,201)(123,208)(124,207)(125,205)(126,206)(127,204)(128,203)(129,210)
(130,209)(131,216)(132,215)(133,213)(134,214)(135,212)(136,211)(137,218)
(138,217)(139,224)(140,223)(141,221)(142,222)(143,220)(144,219)(145,226)
(146,225)(147,232)(148,231)(149,229)(150,230)(151,228)(152,227)(153,234)
(154,233)(155,240)(156,239)(157,237)(158,238)(159,236)(160,235)(161,162)
(163,168)(164,167)(169,170)(171,176)(172,175)(177,178)(179,184)(180,183)
(185,186)(187,192)(188,191)(193,194)(195,200)(196,199);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(240)!( 9, 33)( 10, 34)( 11, 35)( 12, 36)( 13, 37)( 14, 38)( 15, 39)
( 16, 40)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 49, 73)( 50, 74)( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)
( 56, 80)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)
( 64, 72)( 89,113)( 90,114)( 91,115)( 92,116)( 93,117)( 94,118)( 95,119)
( 96,120)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(129,153)(130,154)(131,155)(132,156)(133,157)(134,158)(135,159)
(136,160)(137,145)(138,146)(139,147)(140,148)(141,149)(142,150)(143,151)
(144,152)(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)
(176,200)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(209,233)(210,234)(211,235)(212,236)(213,237)(214,238)(215,239)
(216,240)(217,225)(218,226)(219,227)(220,228)(221,229)(222,230)(223,231)
(224,232);
s1 := Sym(240)!( 1,133)( 2,134)( 3,136)( 4,135)( 5,130)( 6,129)( 7,131)
( 8,132)( 9,125)( 10,126)( 11,128)( 12,127)( 13,122)( 14,121)( 15,123)
( 16,124)( 17,157)( 18,158)( 19,160)( 20,159)( 21,154)( 22,153)( 23,155)
( 24,156)( 25,149)( 26,150)( 27,152)( 28,151)( 29,146)( 30,145)( 31,147)
( 32,148)( 33,141)( 34,142)( 35,144)( 36,143)( 37,138)( 38,137)( 39,139)
( 40,140)( 41,173)( 42,174)( 43,176)( 44,175)( 45,170)( 46,169)( 47,171)
( 48,172)( 49,165)( 50,166)( 51,168)( 52,167)( 53,162)( 54,161)( 55,163)
( 56,164)( 57,197)( 58,198)( 59,200)( 60,199)( 61,194)( 62,193)( 63,195)
( 64,196)( 65,189)( 66,190)( 67,192)( 68,191)( 69,186)( 70,185)( 71,187)
( 72,188)( 73,181)( 74,182)( 75,184)( 76,183)( 77,178)( 78,177)( 79,179)
( 80,180)( 81,213)( 82,214)( 83,216)( 84,215)( 85,210)( 86,209)( 87,211)
( 88,212)( 89,205)( 90,206)( 91,208)( 92,207)( 93,202)( 94,201)( 95,203)
( 96,204)( 97,237)( 98,238)( 99,240)(100,239)(101,234)(102,233)(103,235)
(104,236)(105,229)(106,230)(107,232)(108,231)(109,226)(110,225)(111,227)
(112,228)(113,221)(114,222)(115,224)(116,223)(117,218)(118,217)(119,219)
(120,220);
s2 := Sym(240)!( 3, 6)( 4, 5)( 7, 8)( 11, 14)( 12, 13)( 15, 16)( 19, 22)
( 20, 21)( 23, 24)( 27, 30)( 28, 29)( 31, 32)( 35, 38)( 36, 37)( 39, 40)
( 41, 81)( 42, 82)( 43, 86)( 44, 85)( 45, 84)( 46, 83)( 47, 88)( 48, 87)
( 49, 89)( 50, 90)( 51, 94)( 52, 93)( 53, 92)( 54, 91)( 55, 96)( 56, 95)
( 57, 97)( 58, 98)( 59,102)( 60,101)( 61,100)( 62, 99)( 63,104)( 64,103)
( 65,105)( 66,106)( 67,110)( 68,109)( 69,108)( 70,107)( 71,112)( 72,111)
( 73,113)( 74,114)( 75,118)( 76,117)( 77,116)( 78,115)( 79,120)( 80,119)
(121,122)(123,125)(124,126)(129,130)(131,133)(132,134)(137,138)(139,141)
(140,142)(145,146)(147,149)(148,150)(153,154)(155,157)(156,158)(161,202)
(162,201)(163,205)(164,206)(165,203)(166,204)(167,207)(168,208)(169,210)
(170,209)(171,213)(172,214)(173,211)(174,212)(175,215)(176,216)(177,218)
(178,217)(179,221)(180,222)(181,219)(182,220)(183,223)(184,224)(185,226)
(186,225)(187,229)(188,230)(189,227)(190,228)(191,231)(192,232)(193,234)
(194,233)(195,237)(196,238)(197,235)(198,236)(199,239)(200,240);
s3 := Sym(240)!( 1, 81)( 2, 82)( 3, 87)( 4, 88)( 5, 86)( 6, 85)( 7, 83)
( 8, 84)( 9, 89)( 10, 90)( 11, 95)( 12, 96)( 13, 94)( 14, 93)( 15, 91)
( 16, 92)( 17, 97)( 18, 98)( 19,103)( 20,104)( 21,102)( 22,101)( 23, 99)
( 24,100)( 25,105)( 26,106)( 27,111)( 28,112)( 29,110)( 30,109)( 31,107)
( 32,108)( 33,113)( 34,114)( 35,119)( 36,120)( 37,118)( 38,117)( 39,115)
( 40,116)( 43, 47)( 44, 48)( 45, 46)( 51, 55)( 52, 56)( 53, 54)( 59, 63)
( 60, 64)( 61, 62)( 67, 71)( 68, 72)( 69, 70)( 75, 79)( 76, 80)( 77, 78)
(121,202)(122,201)(123,208)(124,207)(125,205)(126,206)(127,204)(128,203)
(129,210)(130,209)(131,216)(132,215)(133,213)(134,214)(135,212)(136,211)
(137,218)(138,217)(139,224)(140,223)(141,221)(142,222)(143,220)(144,219)
(145,226)(146,225)(147,232)(148,231)(149,229)(150,230)(151,228)(152,227)
(153,234)(154,233)(155,240)(156,239)(157,237)(158,238)(159,236)(160,235)
(161,162)(163,168)(164,167)(169,170)(171,176)(172,175)(177,178)(179,184)
(180,183)(185,186)(187,192)(188,191)(193,194)(195,200)(196,199);
poly := sub<Sym(240)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope