Polytope of Type {2,10,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,6,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 5
Schlafli Type : {2,10,6,6}
Number of vertices, edges, etc : 2, 10, 40, 24, 8
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 : {2,10,6,3}*960
5-fold quotients : {2,2,6,6}*384
10-fold quotients : {2,2,3,6}*192, {2,2,6,3}*192
12-fold quotients : {2,10,2,2}*160
20-fold quotients : {2,2,3,3}*96
24-fold quotients : {2,5,2,2}*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 := ( 7, 19)( 8, 20)( 9, 21)( 10, 22)( 11, 15)( 12, 16)( 13, 17)( 14, 18)
( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 35)( 32, 36)( 33, 37)( 34, 38)
( 47, 59)( 48, 60)( 49, 61)( 50, 62)( 51, 55)( 52, 56)( 53, 57)( 54, 58)
( 67, 79)( 68, 80)( 69, 81)( 70, 82)( 71, 75)( 72, 76)( 73, 77)( 74, 78)
( 87, 99)( 88,100)( 89,101)( 90,102)( 91, 95)( 92, 96)( 93, 97)( 94, 98)
(107,119)(108,120)(109,121)(110,122)(111,115)(112,116)(113,117)(114,118)
(127,139)(128,140)(129,141)(130,142)(131,135)(132,136)(133,137)(134,138)
(147,159)(148,160)(149,161)(150,162)(151,155)(152,156)(153,157)(154,158)
(167,179)(168,180)(169,181)(170,182)(171,175)(172,176)(173,177)(174,178)
(187,199)(188,200)(189,201)(190,202)(191,195)(192,196)(193,197)(194,198)
(207,219)(208,220)(209,221)(210,222)(211,215)(212,216)(213,217)(214,218)
(227,239)(228,240)(229,241)(230,242)(231,235)(232,236)(233,237)(234,238);;
s2 := ( 3, 7)( 4, 9)( 5, 8)( 6, 10)( 11, 19)( 12, 21)( 13, 20)( 14, 22)
( 16, 17)( 23, 47)( 24, 49)( 25, 48)( 26, 50)( 27, 43)( 28, 45)( 29, 44)
( 30, 46)( 31, 59)( 32, 61)( 33, 60)( 34, 62)( 35, 55)( 36, 57)( 37, 56)
( 38, 58)( 39, 51)( 40, 53)( 41, 52)( 42, 54)( 63, 67)( 64, 69)( 65, 68)
( 66, 70)( 71, 79)( 72, 81)( 73, 80)( 74, 82)( 76, 77)( 83,107)( 84,109)
( 85,108)( 86,110)( 87,103)( 88,105)( 89,104)( 90,106)( 91,119)( 92,121)
( 93,120)( 94,122)( 95,115)( 96,117)( 97,116)( 98,118)( 99,111)(100,113)
(101,112)(102,114)(123,127)(124,129)(125,128)(126,130)(131,139)(132,141)
(133,140)(134,142)(136,137)(143,167)(144,169)(145,168)(146,170)(147,163)
(148,165)(149,164)(150,166)(151,179)(152,181)(153,180)(154,182)(155,175)
(156,177)(157,176)(158,178)(159,171)(160,173)(161,172)(162,174)(183,187)
(184,189)(185,188)(186,190)(191,199)(192,201)(193,200)(194,202)(196,197)
(203,227)(204,229)(205,228)(206,230)(207,223)(208,225)(209,224)(210,226)
(211,239)(212,241)(213,240)(214,242)(215,235)(216,237)(217,236)(218,238)
(219,231)(220,233)(221,232)(222,234);;
s3 := ( 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);;
s4 := ( 3, 66)( 4, 64)( 5, 65)( 6, 63)( 7, 70)( 8, 68)( 9, 69)( 10, 67)
( 11, 74)( 12, 72)( 13, 73)( 14, 71)( 15, 78)( 16, 76)( 17, 77)( 18, 75)
( 19, 82)( 20, 80)( 21, 81)( 22, 79)( 23,106)( 24,104)( 25,105)( 26,103)
( 27,110)( 28,108)( 29,109)( 30,107)( 31,114)( 32,112)( 33,113)( 34,111)
( 35,118)( 36,116)( 37,117)( 38,115)( 39,122)( 40,120)( 41,121)( 42,119)
( 43, 86)( 44, 84)( 45, 85)( 46, 83)( 47, 90)( 48, 88)( 49, 89)( 50, 87)
( 51, 94)( 52, 92)( 53, 93)( 54, 91)( 55, 98)( 56, 96)( 57, 97)( 58, 95)
( 59,102)( 60,100)( 61,101)( 62, 99)(123,186)(124,184)(125,185)(126,183)
(127,190)(128,188)(129,189)(130,187)(131,194)(132,192)(133,193)(134,191)
(135,198)(136,196)(137,197)(138,195)(139,202)(140,200)(141,201)(142,199)
(143,226)(144,224)(145,225)(146,223)(147,230)(148,228)(149,229)(150,227)
(151,234)(152,232)(153,233)(154,231)(155,238)(156,236)(157,237)(158,235)
(159,242)(160,240)(161,241)(162,239)(163,206)(164,204)(165,205)(166,203)
(167,210)(168,208)(169,209)(170,207)(171,214)(172,212)(173,213)(174,211)
(175,218)(176,216)(177,217)(178,215)(179,222)(180,220)(181,221)(182,219);;
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*s3*s2*s1*s2*s3*s2, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*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)!( 7, 19)( 8, 20)( 9, 21)( 10, 22)( 11, 15)( 12, 16)( 13, 17)
( 14, 18)( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 35)( 32, 36)( 33, 37)
( 34, 38)( 47, 59)( 48, 60)( 49, 61)( 50, 62)( 51, 55)( 52, 56)( 53, 57)
( 54, 58)( 67, 79)( 68, 80)( 69, 81)( 70, 82)( 71, 75)( 72, 76)( 73, 77)
( 74, 78)( 87, 99)( 88,100)( 89,101)( 90,102)( 91, 95)( 92, 96)( 93, 97)
( 94, 98)(107,119)(108,120)(109,121)(110,122)(111,115)(112,116)(113,117)
(114,118)(127,139)(128,140)(129,141)(130,142)(131,135)(132,136)(133,137)
(134,138)(147,159)(148,160)(149,161)(150,162)(151,155)(152,156)(153,157)
(154,158)(167,179)(168,180)(169,181)(170,182)(171,175)(172,176)(173,177)
(174,178)(187,199)(188,200)(189,201)(190,202)(191,195)(192,196)(193,197)
(194,198)(207,219)(208,220)(209,221)(210,222)(211,215)(212,216)(213,217)
(214,218)(227,239)(228,240)(229,241)(230,242)(231,235)(232,236)(233,237)
(234,238);
s2 := Sym(242)!( 3, 7)( 4, 9)( 5, 8)( 6, 10)( 11, 19)( 12, 21)( 13, 20)
( 14, 22)( 16, 17)( 23, 47)( 24, 49)( 25, 48)( 26, 50)( 27, 43)( 28, 45)
( 29, 44)( 30, 46)( 31, 59)( 32, 61)( 33, 60)( 34, 62)( 35, 55)( 36, 57)
( 37, 56)( 38, 58)( 39, 51)( 40, 53)( 41, 52)( 42, 54)( 63, 67)( 64, 69)
( 65, 68)( 66, 70)( 71, 79)( 72, 81)( 73, 80)( 74, 82)( 76, 77)( 83,107)
( 84,109)( 85,108)( 86,110)( 87,103)( 88,105)( 89,104)( 90,106)( 91,119)
( 92,121)( 93,120)( 94,122)( 95,115)( 96,117)( 97,116)( 98,118)( 99,111)
(100,113)(101,112)(102,114)(123,127)(124,129)(125,128)(126,130)(131,139)
(132,141)(133,140)(134,142)(136,137)(143,167)(144,169)(145,168)(146,170)
(147,163)(148,165)(149,164)(150,166)(151,179)(152,181)(153,180)(154,182)
(155,175)(156,177)(157,176)(158,178)(159,171)(160,173)(161,172)(162,174)
(183,187)(184,189)(185,188)(186,190)(191,199)(192,201)(193,200)(194,202)
(196,197)(203,227)(204,229)(205,228)(206,230)(207,223)(208,225)(209,224)
(210,226)(211,239)(212,241)(213,240)(214,242)(215,235)(216,237)(217,236)
(218,238)(219,231)(220,233)(221,232)(222,234);
s3 := 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);
s4 := Sym(242)!( 3, 66)( 4, 64)( 5, 65)( 6, 63)( 7, 70)( 8, 68)( 9, 69)
( 10, 67)( 11, 74)( 12, 72)( 13, 73)( 14, 71)( 15, 78)( 16, 76)( 17, 77)
( 18, 75)( 19, 82)( 20, 80)( 21, 81)( 22, 79)( 23,106)( 24,104)( 25,105)
( 26,103)( 27,110)( 28,108)( 29,109)( 30,107)( 31,114)( 32,112)( 33,113)
( 34,111)( 35,118)( 36,116)( 37,117)( 38,115)( 39,122)( 40,120)( 41,121)
( 42,119)( 43, 86)( 44, 84)( 45, 85)( 46, 83)( 47, 90)( 48, 88)( 49, 89)
( 50, 87)( 51, 94)( 52, 92)( 53, 93)( 54, 91)( 55, 98)( 56, 96)( 57, 97)
( 58, 95)( 59,102)( 60,100)( 61,101)( 62, 99)(123,186)(124,184)(125,185)
(126,183)(127,190)(128,188)(129,189)(130,187)(131,194)(132,192)(133,193)
(134,191)(135,198)(136,196)(137,197)(138,195)(139,202)(140,200)(141,201)
(142,199)(143,226)(144,224)(145,225)(146,223)(147,230)(148,228)(149,229)
(150,227)(151,234)(152,232)(153,233)(154,231)(155,238)(156,236)(157,237)
(158,235)(159,242)(160,240)(161,241)(162,239)(163,206)(164,204)(165,205)
(166,203)(167,210)(168,208)(169,209)(170,207)(171,214)(172,212)(173,213)
(174,211)(175,218)(176,216)(177,217)(178,215)(179,222)(180,220)(181,221)
(182,219);
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*s3*s2*s1*s2*s3*s2,
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*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