Polytope of Type {10,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,6,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,240213)
Rank : 4
Schlafli Type : {10,6,6}
Number of vertices, edges, etc : 10, 80, 48, 16
Order of s0s1s2s3 : 40
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {10,6,6}*960
4-fold quotients : {10,6,3}*480
5-fold quotients : {2,6,6}*384b
10-fold quotients : {2,6,6}*192
20-fold quotients : {2,3,6}*96, {2,6,3}*96
24-fold quotients : {10,2,2}*80
40-fold quotients : {2,3,3}*48
48-fold quotients : {5,2,2}*40
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
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, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 15)( 6, 16)( 7, 13)( 8, 14)
( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 39)( 22, 40)( 23, 37)( 24, 38)
( 27, 28)( 29, 31)( 30, 32)( 41, 89)( 42, 90)( 43, 92)( 44, 91)( 45, 95)
( 46, 96)( 47, 93)( 48, 94)( 49, 81)( 50, 82)( 51, 84)( 52, 83)( 53, 87)
( 54, 88)( 55, 85)( 56, 86)( 57,113)( 58,114)( 59,116)( 60,115)( 61,119)
( 62,120)( 63,117)( 64,118)( 65,105)( 66,106)( 67,108)( 68,107)( 69,111)
( 70,112)( 71,109)( 72,110)( 73, 97)( 74, 98)( 75,100)( 76, 99)( 77,103)
( 78,104)( 79,101)( 80,102)(121,130)(122,129)(123,131)(124,132)(125,136)
(126,135)(127,134)(128,133)(137,154)(138,153)(139,155)(140,156)(141,160)
(142,159)(143,158)(144,157)(145,146)(149,152)(150,151)(161,210)(162,209)
(163,211)(164,212)(165,216)(166,215)(167,214)(168,213)(169,202)(170,201)
(171,203)(172,204)(173,208)(174,207)(175,206)(176,205)(177,234)(178,233)
(179,235)(180,236)(181,240)(182,239)(183,238)(184,237)(185,226)(186,225)
(187,227)(188,228)(189,232)(190,231)(191,230)(192,229)(193,218)(194,217)
(195,219)(196,220)(197,224)(198,223)(199,222)(200,221);;
s2 := ( 1, 41)( 2, 42)( 3, 47)( 4, 48)( 5, 46)( 6, 45)( 7, 43)( 8, 44)
( 9, 49)( 10, 50)( 11, 55)( 12, 56)( 13, 54)( 14, 53)( 15, 51)( 16, 52)
( 17, 57)( 18, 58)( 19, 63)( 20, 64)( 21, 62)( 22, 61)( 23, 59)( 24, 60)
( 25, 65)( 26, 66)( 27, 71)( 28, 72)( 29, 70)( 30, 69)( 31, 67)( 32, 68)
( 33, 73)( 34, 74)( 35, 79)( 36, 80)( 37, 78)( 38, 77)( 39, 75)( 40, 76)
( 83, 87)( 84, 88)( 85, 86)( 91, 95)( 92, 96)( 93, 94)( 99,103)(100,104)
(101,102)(107,111)(108,112)(109,110)(115,119)(116,120)(117,118)(121,161)
(122,162)(123,167)(124,168)(125,166)(126,165)(127,163)(128,164)(129,169)
(130,170)(131,175)(132,176)(133,174)(134,173)(135,171)(136,172)(137,177)
(138,178)(139,183)(140,184)(141,182)(142,181)(143,179)(144,180)(145,185)
(146,186)(147,191)(148,192)(149,190)(150,189)(151,187)(152,188)(153,193)
(154,194)(155,199)(156,200)(157,198)(158,197)(159,195)(160,196)(203,207)
(204,208)(205,206)(211,215)(212,216)(213,214)(219,223)(220,224)(221,222)
(227,231)(228,232)(229,230)(235,239)(236,240)(237,238);;
s3 := ( 1,123)( 2,124)( 3,121)( 4,122)( 5,126)( 6,125)( 7,127)( 8,128)
( 9,131)( 10,132)( 11,129)( 12,130)( 13,134)( 14,133)( 15,135)( 16,136)
( 17,139)( 18,140)( 19,137)( 20,138)( 21,142)( 22,141)( 23,143)( 24,144)
( 25,147)( 26,148)( 27,145)( 28,146)( 29,150)( 30,149)( 31,151)( 32,152)
( 33,155)( 34,156)( 35,153)( 36,154)( 37,158)( 38,157)( 39,159)( 40,160)
( 41,203)( 42,204)( 43,201)( 44,202)( 45,206)( 46,205)( 47,207)( 48,208)
( 49,211)( 50,212)( 51,209)( 52,210)( 53,214)( 54,213)( 55,215)( 56,216)
( 57,219)( 58,220)( 59,217)( 60,218)( 61,222)( 62,221)( 63,223)( 64,224)
( 65,227)( 66,228)( 67,225)( 68,226)( 69,230)( 70,229)( 71,231)( 72,232)
( 73,235)( 74,236)( 75,233)( 76,234)( 77,238)( 78,237)( 79,239)( 80,240)
( 81,163)( 82,164)( 83,161)( 84,162)( 85,166)( 86,165)( 87,167)( 88,168)
( 89,171)( 90,172)( 91,169)( 92,170)( 93,174)( 94,173)( 95,175)( 96,176)
( 97,179)( 98,180)( 99,177)(100,178)(101,182)(102,181)(103,183)(104,184)
(105,187)(106,188)(107,185)(108,186)(109,190)(110,189)(111,191)(112,192)
(113,195)(114,196)(115,193)(116,194)(117,198)(118,197)(119,199)(120,200);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*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, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 15)( 6, 16)( 7, 13)
( 8, 14)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 39)( 22, 40)( 23, 37)
( 24, 38)( 27, 28)( 29, 31)( 30, 32)( 41, 89)( 42, 90)( 43, 92)( 44, 91)
( 45, 95)( 46, 96)( 47, 93)( 48, 94)( 49, 81)( 50, 82)( 51, 84)( 52, 83)
( 53, 87)( 54, 88)( 55, 85)( 56, 86)( 57,113)( 58,114)( 59,116)( 60,115)
( 61,119)( 62,120)( 63,117)( 64,118)( 65,105)( 66,106)( 67,108)( 68,107)
( 69,111)( 70,112)( 71,109)( 72,110)( 73, 97)( 74, 98)( 75,100)( 76, 99)
( 77,103)( 78,104)( 79,101)( 80,102)(121,130)(122,129)(123,131)(124,132)
(125,136)(126,135)(127,134)(128,133)(137,154)(138,153)(139,155)(140,156)
(141,160)(142,159)(143,158)(144,157)(145,146)(149,152)(150,151)(161,210)
(162,209)(163,211)(164,212)(165,216)(166,215)(167,214)(168,213)(169,202)
(170,201)(171,203)(172,204)(173,208)(174,207)(175,206)(176,205)(177,234)
(178,233)(179,235)(180,236)(181,240)(182,239)(183,238)(184,237)(185,226)
(186,225)(187,227)(188,228)(189,232)(190,231)(191,230)(192,229)(193,218)
(194,217)(195,219)(196,220)(197,224)(198,223)(199,222)(200,221);
s2 := Sym(240)!( 1, 41)( 2, 42)( 3, 47)( 4, 48)( 5, 46)( 6, 45)( 7, 43)
( 8, 44)( 9, 49)( 10, 50)( 11, 55)( 12, 56)( 13, 54)( 14, 53)( 15, 51)
( 16, 52)( 17, 57)( 18, 58)( 19, 63)( 20, 64)( 21, 62)( 22, 61)( 23, 59)
( 24, 60)( 25, 65)( 26, 66)( 27, 71)( 28, 72)( 29, 70)( 30, 69)( 31, 67)
( 32, 68)( 33, 73)( 34, 74)( 35, 79)( 36, 80)( 37, 78)( 38, 77)( 39, 75)
( 40, 76)( 83, 87)( 84, 88)( 85, 86)( 91, 95)( 92, 96)( 93, 94)( 99,103)
(100,104)(101,102)(107,111)(108,112)(109,110)(115,119)(116,120)(117,118)
(121,161)(122,162)(123,167)(124,168)(125,166)(126,165)(127,163)(128,164)
(129,169)(130,170)(131,175)(132,176)(133,174)(134,173)(135,171)(136,172)
(137,177)(138,178)(139,183)(140,184)(141,182)(142,181)(143,179)(144,180)
(145,185)(146,186)(147,191)(148,192)(149,190)(150,189)(151,187)(152,188)
(153,193)(154,194)(155,199)(156,200)(157,198)(158,197)(159,195)(160,196)
(203,207)(204,208)(205,206)(211,215)(212,216)(213,214)(219,223)(220,224)
(221,222)(227,231)(228,232)(229,230)(235,239)(236,240)(237,238);
s3 := Sym(240)!( 1,123)( 2,124)( 3,121)( 4,122)( 5,126)( 6,125)( 7,127)
( 8,128)( 9,131)( 10,132)( 11,129)( 12,130)( 13,134)( 14,133)( 15,135)
( 16,136)( 17,139)( 18,140)( 19,137)( 20,138)( 21,142)( 22,141)( 23,143)
( 24,144)( 25,147)( 26,148)( 27,145)( 28,146)( 29,150)( 30,149)( 31,151)
( 32,152)( 33,155)( 34,156)( 35,153)( 36,154)( 37,158)( 38,157)( 39,159)
( 40,160)( 41,203)( 42,204)( 43,201)( 44,202)( 45,206)( 46,205)( 47,207)
( 48,208)( 49,211)( 50,212)( 51,209)( 52,210)( 53,214)( 54,213)( 55,215)
( 56,216)( 57,219)( 58,220)( 59,217)( 60,218)( 61,222)( 62,221)( 63,223)
( 64,224)( 65,227)( 66,228)( 67,225)( 68,226)( 69,230)( 70,229)( 71,231)
( 72,232)( 73,235)( 74,236)( 75,233)( 76,234)( 77,238)( 78,237)( 79,239)
( 80,240)( 81,163)( 82,164)( 83,161)( 84,162)( 85,166)( 86,165)( 87,167)
( 88,168)( 89,171)( 90,172)( 91,169)( 92,170)( 93,174)( 94,173)( 95,175)
( 96,176)( 97,179)( 98,180)( 99,177)(100,178)(101,182)(102,181)(103,183)
(104,184)(105,187)(106,188)(107,185)(108,186)(109,190)(110,189)(111,191)
(112,192)(113,195)(114,196)(115,193)(116,194)(117,198)(118,197)(119,199)
(120,200);
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,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*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