Polytope of Type {2,10,4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,4,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 5
Schlafli Type : {2,10,4,6}
Number of vertices, edges, etc : 2, 10, 40, 24, 12
Order of s0s1s2s3s4 : 30
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
4-fold quotients : {2,10,2,6}*480
5-fold quotients : {2,2,4,6}*384
8-fold quotients : {2,5,2,6}*240, {2,10,2,3}*240
10-fold quotients : {2,2,4,3}*192, {2,2,4,6}*192b, {2,2,4,6}*192c
12-fold quotients : {2,10,2,2}*160
16-fold quotients : {2,5,2,3}*120
20-fold quotients : {2,2,4,3}*96, {2,2,2,6}*96
24-fold quotients : {2,5,2,2}*80
40-fold quotients : {2,2,2,3}*48
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 := ( 3,129)( 4,130)( 5,127)( 6,128)( 7,125)( 8,126)( 9,123)( 10,124)
( 11,141)( 12,142)( 13,139)( 14,140)( 15,137)( 16,138)( 17,135)( 18,136)
( 19,133)( 20,134)( 21,131)( 22,132)( 23,149)( 24,150)( 25,147)( 26,148)
( 27,145)( 28,146)( 29,143)( 30,144)( 31,161)( 32,162)( 33,159)( 34,160)
( 35,157)( 36,158)( 37,155)( 38,156)( 39,153)( 40,154)( 41,151)( 42,152)
( 43,169)( 44,170)( 45,167)( 46,168)( 47,165)( 48,166)( 49,163)( 50,164)
( 51,181)( 52,182)( 53,179)( 54,180)( 55,177)( 56,178)( 57,175)( 58,176)
( 59,173)( 60,174)( 61,171)( 62,172)( 63,189)( 64,190)( 65,187)( 66,188)
( 67,185)( 68,186)( 69,183)( 70,184)( 71,201)( 72,202)( 73,199)( 74,200)
( 75,197)( 76,198)( 77,195)( 78,196)( 79,193)( 80,194)( 81,191)( 82,192)
( 83,209)( 84,210)( 85,207)( 86,208)( 87,205)( 88,206)( 89,203)( 90,204)
( 91,221)( 92,222)( 93,219)( 94,220)( 95,217)( 96,218)( 97,215)( 98,216)
( 99,213)(100,214)(101,211)(102,212)(103,229)(104,230)(105,227)(106,228)
(107,225)(108,226)(109,223)(110,224)(111,241)(112,242)(113,239)(114,240)
(115,237)(116,238)(117,235)(118,236)(119,233)(120,234)(121,231)(122,232);;
s3 := ( 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);;
s4 := ( 3,103)( 4,106)( 5,105)( 6,104)( 7,107)( 8,110)( 9,109)( 10,108)
( 11,111)( 12,114)( 13,113)( 14,112)( 15,115)( 16,118)( 17,117)( 18,116)
( 19,119)( 20,122)( 21,121)( 22,120)( 23, 83)( 24, 86)( 25, 85)( 26, 84)
( 27, 87)( 28, 90)( 29, 89)( 30, 88)( 31, 91)( 32, 94)( 33, 93)( 34, 92)
( 35, 95)( 36, 98)( 37, 97)( 38, 96)( 39, 99)( 40,102)( 41,101)( 42,100)
( 43, 63)( 44, 66)( 45, 65)( 46, 64)( 47, 67)( 48, 70)( 49, 69)( 50, 68)
( 51, 71)( 52, 74)( 53, 73)( 54, 72)( 55, 75)( 56, 78)( 57, 77)( 58, 76)
( 59, 79)( 60, 82)( 61, 81)( 62, 80)(123,223)(124,226)(125,225)(126,224)
(127,227)(128,230)(129,229)(130,228)(131,231)(132,234)(133,233)(134,232)
(135,235)(136,238)(137,237)(138,236)(139,239)(140,242)(141,241)(142,240)
(143,203)(144,206)(145,205)(146,204)(147,207)(148,210)(149,209)(150,208)
(151,211)(152,214)(153,213)(154,212)(155,215)(156,218)(157,217)(158,216)
(159,219)(160,222)(161,221)(162,220)(163,183)(164,186)(165,185)(166,184)
(167,187)(168,190)(169,189)(170,188)(171,191)(172,194)(173,193)(174,192)
(175,195)(176,198)(177,197)(178,196)(179,199)(180,202)(181,201)(182,200);;
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, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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)!( 3,129)( 4,130)( 5,127)( 6,128)( 7,125)( 8,126)( 9,123)
( 10,124)( 11,141)( 12,142)( 13,139)( 14,140)( 15,137)( 16,138)( 17,135)
( 18,136)( 19,133)( 20,134)( 21,131)( 22,132)( 23,149)( 24,150)( 25,147)
( 26,148)( 27,145)( 28,146)( 29,143)( 30,144)( 31,161)( 32,162)( 33,159)
( 34,160)( 35,157)( 36,158)( 37,155)( 38,156)( 39,153)( 40,154)( 41,151)
( 42,152)( 43,169)( 44,170)( 45,167)( 46,168)( 47,165)( 48,166)( 49,163)
( 50,164)( 51,181)( 52,182)( 53,179)( 54,180)( 55,177)( 56,178)( 57,175)
( 58,176)( 59,173)( 60,174)( 61,171)( 62,172)( 63,189)( 64,190)( 65,187)
( 66,188)( 67,185)( 68,186)( 69,183)( 70,184)( 71,201)( 72,202)( 73,199)
( 74,200)( 75,197)( 76,198)( 77,195)( 78,196)( 79,193)( 80,194)( 81,191)
( 82,192)( 83,209)( 84,210)( 85,207)( 86,208)( 87,205)( 88,206)( 89,203)
( 90,204)( 91,221)( 92,222)( 93,219)( 94,220)( 95,217)( 96,218)( 97,215)
( 98,216)( 99,213)(100,214)(101,211)(102,212)(103,229)(104,230)(105,227)
(106,228)(107,225)(108,226)(109,223)(110,224)(111,241)(112,242)(113,239)
(114,240)(115,237)(116,238)(117,235)(118,236)(119,233)(120,234)(121,231)
(122,232);
s3 := 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);
s4 := Sym(242)!( 3,103)( 4,106)( 5,105)( 6,104)( 7,107)( 8,110)( 9,109)
( 10,108)( 11,111)( 12,114)( 13,113)( 14,112)( 15,115)( 16,118)( 17,117)
( 18,116)( 19,119)( 20,122)( 21,121)( 22,120)( 23, 83)( 24, 86)( 25, 85)
( 26, 84)( 27, 87)( 28, 90)( 29, 89)( 30, 88)( 31, 91)( 32, 94)( 33, 93)
( 34, 92)( 35, 95)( 36, 98)( 37, 97)( 38, 96)( 39, 99)( 40,102)( 41,101)
( 42,100)( 43, 63)( 44, 66)( 45, 65)( 46, 64)( 47, 67)( 48, 70)( 49, 69)
( 50, 68)( 51, 71)( 52, 74)( 53, 73)( 54, 72)( 55, 75)( 56, 78)( 57, 77)
( 58, 76)( 59, 79)( 60, 82)( 61, 81)( 62, 80)(123,223)(124,226)(125,225)
(126,224)(127,227)(128,230)(129,229)(130,228)(131,231)(132,234)(133,233)
(134,232)(135,235)(136,238)(137,237)(138,236)(139,239)(140,242)(141,241)
(142,240)(143,203)(144,206)(145,205)(146,204)(147,207)(148,210)(149,209)
(150,208)(151,211)(152,214)(153,213)(154,212)(155,215)(156,218)(157,217)
(158,216)(159,219)(160,222)(161,221)(162,220)(163,183)(164,186)(165,185)
(166,184)(167,187)(168,190)(169,189)(170,188)(171,191)(172,194)(173,193)
(174,192)(175,195)(176,198)(177,197)(178,196)(179,199)(180,202)(181,201)
(182,200);
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,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope