Polytope of Type {2,6,6,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,10}*1920
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 5
Schlafli Type : {2,6,6,10}
Number of vertices, edges, etc : 2, 8, 24, 40, 10
Order of s0s1s2s3s4 : 20
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 : {2,3,6,10}*960
5-fold quotients : {2,6,6,2}*384
10-fold quotients : {2,3,6,2}*192, {2,6,3,2}*192
12-fold quotients : {2,2,2,10}*160
20-fold quotients : {2,3,3,2}*96
24-fold quotients : {2,2,2,5}*80
60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 8, 9)( 12, 13)( 16, 17)( 20, 21)( 23, 43)( 24, 45)( 25, 44)
( 26, 46)( 27, 47)( 28, 49)( 29, 48)( 30, 50)( 31, 51)( 32, 53)( 33, 52)
( 34, 54)( 35, 55)( 36, 57)( 37, 56)( 38, 58)( 39, 59)( 40, 61)( 41, 60)
( 42, 62)( 64, 65)( 68, 69)( 72, 73)( 76, 77)( 80, 81)( 83,103)( 84,105)
( 85,104)( 86,106)( 87,107)( 88,109)( 89,108)( 90,110)( 91,111)( 92,113)
( 93,112)( 94,114)( 95,115)( 96,117)( 97,116)( 98,118)( 99,119)(100,121)
(101,120)(102,122)(124,125)(128,129)(132,133)(136,137)(140,141)(143,163)
(144,165)(145,164)(146,166)(147,167)(148,169)(149,168)(150,170)(151,171)
(152,173)(153,172)(154,174)(155,175)(156,177)(157,176)(158,178)(159,179)
(160,181)(161,180)(162,182)(184,185)(188,189)(192,193)(196,197)(200,201)
(203,223)(204,225)(205,224)(206,226)(207,227)(208,229)(209,228)(210,230)
(211,231)(212,233)(213,232)(214,234)(215,235)(216,237)(217,236)(218,238)
(219,239)(220,241)(221,240)(222,242);;
s2 := ( 3,143)( 4,144)( 5,146)( 6,145)( 7,147)( 8,148)( 9,150)( 10,149)
( 11,151)( 12,152)( 13,154)( 14,153)( 15,155)( 16,156)( 17,158)( 18,157)
( 19,159)( 20,160)( 21,162)( 22,161)( 23,123)( 24,124)( 25,126)( 26,125)
( 27,127)( 28,128)( 29,130)( 30,129)( 31,131)( 32,132)( 33,134)( 34,133)
( 35,135)( 36,136)( 37,138)( 38,137)( 39,139)( 40,140)( 41,142)( 42,141)
( 43,163)( 44,164)( 45,166)( 46,165)( 47,167)( 48,168)( 49,170)( 50,169)
( 51,171)( 52,172)( 53,174)( 54,173)( 55,175)( 56,176)( 57,178)( 58,177)
( 59,179)( 60,180)( 61,182)( 62,181)( 63,203)( 64,204)( 65,206)( 66,205)
( 67,207)( 68,208)( 69,210)( 70,209)( 71,211)( 72,212)( 73,214)( 74,213)
( 75,215)( 76,216)( 77,218)( 78,217)( 79,219)( 80,220)( 81,222)( 82,221)
( 83,183)( 84,184)( 85,186)( 86,185)( 87,187)( 88,188)( 89,190)( 90,189)
( 91,191)( 92,192)( 93,194)( 94,193)( 95,195)( 96,196)( 97,198)( 98,197)
( 99,199)(100,200)(101,202)(102,201)(103,223)(104,224)(105,226)(106,225)
(107,227)(108,228)(109,230)(110,229)(111,231)(112,232)(113,234)(114,233)
(115,235)(116,236)(117,238)(118,237)(119,239)(120,240)(121,242)(122,241);;
s3 := ( 3, 6)( 7, 22)( 8, 20)( 9, 21)( 10, 19)( 11, 18)( 12, 16)( 13, 17)
( 14, 15)( 23, 46)( 24, 44)( 25, 45)( 26, 43)( 27, 62)( 28, 60)( 29, 61)
( 30, 59)( 31, 58)( 32, 56)( 33, 57)( 34, 55)( 35, 54)( 36, 52)( 37, 53)
( 38, 51)( 39, 50)( 40, 48)( 41, 49)( 42, 47)( 63, 66)( 67, 82)( 68, 80)
( 69, 81)( 70, 79)( 71, 78)( 72, 76)( 73, 77)( 74, 75)( 83,106)( 84,104)
( 85,105)( 86,103)( 87,122)( 88,120)( 89,121)( 90,119)( 91,118)( 92,116)
( 93,117)( 94,115)( 95,114)( 96,112)( 97,113)( 98,111)( 99,110)(100,108)
(101,109)(102,107)(123,126)(127,142)(128,140)(129,141)(130,139)(131,138)
(132,136)(133,137)(134,135)(143,166)(144,164)(145,165)(146,163)(147,182)
(148,180)(149,181)(150,179)(151,178)(152,176)(153,177)(154,175)(155,174)
(156,172)(157,173)(158,171)(159,170)(160,168)(161,169)(162,167)(183,186)
(187,202)(188,200)(189,201)(190,199)(191,198)(192,196)(193,197)(194,195)
(203,226)(204,224)(205,225)(206,223)(207,242)(208,240)(209,241)(210,239)
(211,238)(212,236)(213,237)(214,235)(215,234)(216,232)(217,233)(218,231)
(219,230)(220,228)(221,229)(222,227);;
s4 := ( 3, 67)( 4, 68)( 5, 69)( 6, 70)( 7, 63)( 8, 64)( 9, 65)( 10, 66)
( 11, 79)( 12, 80)( 13, 81)( 14, 82)( 15, 75)( 16, 76)( 17, 77)( 18, 78)
( 19, 71)( 20, 72)( 21, 73)( 22, 74)( 23, 87)( 24, 88)( 25, 89)( 26, 90)
( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 99)( 32,100)( 33,101)( 34,102)
( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 91)( 40, 92)( 41, 93)( 42, 94)
( 43,107)( 44,108)( 45,109)( 46,110)( 47,103)( 48,104)( 49,105)( 50,106)
( 51,119)( 52,120)( 53,121)( 54,122)( 55,115)( 56,116)( 57,117)( 58,118)
( 59,111)( 60,112)( 61,113)( 62,114)(123,187)(124,188)(125,189)(126,190)
(127,183)(128,184)(129,185)(130,186)(131,199)(132,200)(133,201)(134,202)
(135,195)(136,196)(137,197)(138,198)(139,191)(140,192)(141,193)(142,194)
(143,207)(144,208)(145,209)(146,210)(147,203)(148,204)(149,205)(150,206)
(151,219)(152,220)(153,221)(154,222)(155,215)(156,216)(157,217)(158,218)
(159,211)(160,212)(161,213)(162,214)(163,227)(164,228)(165,229)(166,230)
(167,223)(168,224)(169,225)(170,226)(171,239)(172,240)(173,241)(174,242)
(175,235)(176,236)(177,237)(178,238)(179,231)(180,232)(181,233)(182,234);;
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,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*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)!( 4, 5)( 8, 9)( 12, 13)( 16, 17)( 20, 21)( 23, 43)( 24, 45)
( 25, 44)( 26, 46)( 27, 47)( 28, 49)( 29, 48)( 30, 50)( 31, 51)( 32, 53)
( 33, 52)( 34, 54)( 35, 55)( 36, 57)( 37, 56)( 38, 58)( 39, 59)( 40, 61)
( 41, 60)( 42, 62)( 64, 65)( 68, 69)( 72, 73)( 76, 77)( 80, 81)( 83,103)
( 84,105)( 85,104)( 86,106)( 87,107)( 88,109)( 89,108)( 90,110)( 91,111)
( 92,113)( 93,112)( 94,114)( 95,115)( 96,117)( 97,116)( 98,118)( 99,119)
(100,121)(101,120)(102,122)(124,125)(128,129)(132,133)(136,137)(140,141)
(143,163)(144,165)(145,164)(146,166)(147,167)(148,169)(149,168)(150,170)
(151,171)(152,173)(153,172)(154,174)(155,175)(156,177)(157,176)(158,178)
(159,179)(160,181)(161,180)(162,182)(184,185)(188,189)(192,193)(196,197)
(200,201)(203,223)(204,225)(205,224)(206,226)(207,227)(208,229)(209,228)
(210,230)(211,231)(212,233)(213,232)(214,234)(215,235)(216,237)(217,236)
(218,238)(219,239)(220,241)(221,240)(222,242);
s2 := Sym(242)!( 3,143)( 4,144)( 5,146)( 6,145)( 7,147)( 8,148)( 9,150)
( 10,149)( 11,151)( 12,152)( 13,154)( 14,153)( 15,155)( 16,156)( 17,158)
( 18,157)( 19,159)( 20,160)( 21,162)( 22,161)( 23,123)( 24,124)( 25,126)
( 26,125)( 27,127)( 28,128)( 29,130)( 30,129)( 31,131)( 32,132)( 33,134)
( 34,133)( 35,135)( 36,136)( 37,138)( 38,137)( 39,139)( 40,140)( 41,142)
( 42,141)( 43,163)( 44,164)( 45,166)( 46,165)( 47,167)( 48,168)( 49,170)
( 50,169)( 51,171)( 52,172)( 53,174)( 54,173)( 55,175)( 56,176)( 57,178)
( 58,177)( 59,179)( 60,180)( 61,182)( 62,181)( 63,203)( 64,204)( 65,206)
( 66,205)( 67,207)( 68,208)( 69,210)( 70,209)( 71,211)( 72,212)( 73,214)
( 74,213)( 75,215)( 76,216)( 77,218)( 78,217)( 79,219)( 80,220)( 81,222)
( 82,221)( 83,183)( 84,184)( 85,186)( 86,185)( 87,187)( 88,188)( 89,190)
( 90,189)( 91,191)( 92,192)( 93,194)( 94,193)( 95,195)( 96,196)( 97,198)
( 98,197)( 99,199)(100,200)(101,202)(102,201)(103,223)(104,224)(105,226)
(106,225)(107,227)(108,228)(109,230)(110,229)(111,231)(112,232)(113,234)
(114,233)(115,235)(116,236)(117,238)(118,237)(119,239)(120,240)(121,242)
(122,241);
s3 := Sym(242)!( 3, 6)( 7, 22)( 8, 20)( 9, 21)( 10, 19)( 11, 18)( 12, 16)
( 13, 17)( 14, 15)( 23, 46)( 24, 44)( 25, 45)( 26, 43)( 27, 62)( 28, 60)
( 29, 61)( 30, 59)( 31, 58)( 32, 56)( 33, 57)( 34, 55)( 35, 54)( 36, 52)
( 37, 53)( 38, 51)( 39, 50)( 40, 48)( 41, 49)( 42, 47)( 63, 66)( 67, 82)
( 68, 80)( 69, 81)( 70, 79)( 71, 78)( 72, 76)( 73, 77)( 74, 75)( 83,106)
( 84,104)( 85,105)( 86,103)( 87,122)( 88,120)( 89,121)( 90,119)( 91,118)
( 92,116)( 93,117)( 94,115)( 95,114)( 96,112)( 97,113)( 98,111)( 99,110)
(100,108)(101,109)(102,107)(123,126)(127,142)(128,140)(129,141)(130,139)
(131,138)(132,136)(133,137)(134,135)(143,166)(144,164)(145,165)(146,163)
(147,182)(148,180)(149,181)(150,179)(151,178)(152,176)(153,177)(154,175)
(155,174)(156,172)(157,173)(158,171)(159,170)(160,168)(161,169)(162,167)
(183,186)(187,202)(188,200)(189,201)(190,199)(191,198)(192,196)(193,197)
(194,195)(203,226)(204,224)(205,225)(206,223)(207,242)(208,240)(209,241)
(210,239)(211,238)(212,236)(213,237)(214,235)(215,234)(216,232)(217,233)
(218,231)(219,230)(220,228)(221,229)(222,227);
s4 := Sym(242)!( 3, 67)( 4, 68)( 5, 69)( 6, 70)( 7, 63)( 8, 64)( 9, 65)
( 10, 66)( 11, 79)( 12, 80)( 13, 81)( 14, 82)( 15, 75)( 16, 76)( 17, 77)
( 18, 78)( 19, 71)( 20, 72)( 21, 73)( 22, 74)( 23, 87)( 24, 88)( 25, 89)
( 26, 90)( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 99)( 32,100)( 33,101)
( 34,102)( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 91)( 40, 92)( 41, 93)
( 42, 94)( 43,107)( 44,108)( 45,109)( 46,110)( 47,103)( 48,104)( 49,105)
( 50,106)( 51,119)( 52,120)( 53,121)( 54,122)( 55,115)( 56,116)( 57,117)
( 58,118)( 59,111)( 60,112)( 61,113)( 62,114)(123,187)(124,188)(125,189)
(126,190)(127,183)(128,184)(129,185)(130,186)(131,199)(132,200)(133,201)
(134,202)(135,195)(136,196)(137,197)(138,198)(139,191)(140,192)(141,193)
(142,194)(143,207)(144,208)(145,209)(146,210)(147,203)(148,204)(149,205)
(150,206)(151,219)(152,220)(153,221)(154,222)(155,215)(156,216)(157,217)
(158,218)(159,211)(160,212)(161,213)(162,214)(163,227)(164,228)(165,229)
(166,230)(167,223)(168,224)(169,225)(170,226)(171,239)(172,240)(173,241)
(174,242)(175,235)(176,236)(177,237)(178,238)(179,231)(180,232)(181,233)
(182,234);
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, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*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