Polytope of Type {10,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,6}*960
if this polytope has a name.
Group : SmallGroup(960,11372)
Rank : 4
Schlafli Type : {10,4,6}
Number of vertices, edges, etc : 10, 40, 24, 12
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,4,6,2} of size 1920
Vertex Figure Of :
   {2,10,4,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,4,3}*480
   4-fold quotients : {10,2,6}*240
   5-fold quotients : {2,4,6}*192
   8-fold quotients : {5,2,6}*120, {10,2,3}*120
   10-fold quotients : {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   12-fold quotients : {10,2,2}*80
   16-fold quotients : {5,2,3}*60
   20-fold quotients : {2,4,3}*48, {2,2,6}*48
   24-fold quotients : {5,2,2}*40
   40-fold quotients : {2,2,3}*24
   60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,4,12}*1920b, {20,4,6}*1920b, {10,4,6}*1920, {10,4,12}*1920c, {10,8,6}*1920a, {10,8,6}*1920b
Permutation Representation (GAP) :

s0 := (  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)( 12, 16)
( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)( 32, 36)
( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)( 52, 56)
( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)
( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)(112,116)
(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)(132,136)
(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)(152,156)
(165,177)(166,178)(167,179)(168,180)(169,173)(170,174)(171,175)(172,176)
(185,197)(186,198)(187,199)(188,200)(189,193)(190,194)(191,195)(192,196)
(205,217)(206,218)(207,219)(208,220)(209,213)(210,214)(211,215)(212,216)
(225,237)(226,238)(227,239)(228,240)(229,233)(230,234)(231,235)(232,236);;
s1 := (  1,127)(  2,128)(  3,125)(  4,126)(  5,123)(  6,124)(  7,121)(  8,122)
(  9,139)( 10,140)( 11,137)( 12,138)( 13,135)( 14,136)( 15,133)( 16,134)
( 17,131)( 18,132)( 19,129)( 20,130)( 21,147)( 22,148)( 23,145)( 24,146)
( 25,143)( 26,144)( 27,141)( 28,142)( 29,159)( 30,160)( 31,157)( 32,158)
( 33,155)( 34,156)( 35,153)( 36,154)( 37,151)( 38,152)( 39,149)( 40,150)
( 41,167)( 42,168)( 43,165)( 44,166)( 45,163)( 46,164)( 47,161)( 48,162)
( 49,179)( 50,180)( 51,177)( 52,178)( 53,175)( 54,176)( 55,173)( 56,174)
( 57,171)( 58,172)( 59,169)( 60,170)( 61,187)( 62,188)( 63,185)( 64,186)
( 65,183)( 66,184)( 67,181)( 68,182)( 69,199)( 70,200)( 71,197)( 72,198)
( 73,195)( 74,196)( 75,193)( 76,194)( 77,191)( 78,192)( 79,189)( 80,190)
( 81,207)( 82,208)( 83,205)( 84,206)( 85,203)( 86,204)( 87,201)( 88,202)
( 89,219)( 90,220)( 91,217)( 92,218)( 93,215)( 94,216)( 95,213)( 96,214)
( 97,211)( 98,212)( 99,209)(100,210)(101,227)(102,228)(103,225)(104,226)
(105,223)(106,224)(107,221)(108,222)(109,239)(110,240)(111,237)(112,238)
(113,235)(114,236)(115,233)(116,234)(117,231)(118,232)(119,229)(120,230);;
s2 := (  2,  3)(  6,  7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)( 23, 42)
( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)( 31, 50)
( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)( 39, 58)
( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)( 82,103)
( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)( 90,111)
( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)( 98,119)
( 99,118)(100,120)(122,123)(126,127)(130,131)(134,135)(138,139)(141,161)
(142,163)(143,162)(144,164)(145,165)(146,167)(147,166)(148,168)(149,169)
(150,171)(151,170)(152,172)(153,173)(154,175)(155,174)(156,176)(157,177)
(158,179)(159,178)(160,180)(182,183)(186,187)(190,191)(194,195)(198,199)
(201,221)(202,223)(203,222)(204,224)(205,225)(206,227)(207,226)(208,228)
(209,229)(210,231)(211,230)(212,232)(213,233)(214,235)(215,234)(216,236)
(217,237)(218,239)(219,238)(220,240);;
s3 := (  1,101)(  2,104)(  3,103)(  4,102)(  5,105)(  6,108)(  7,107)(  8,106)
(  9,109)( 10,112)( 11,111)( 12,110)( 13,113)( 14,116)( 15,115)( 16,114)
( 17,117)( 18,120)( 19,119)( 20,118)( 21, 81)( 22, 84)( 23, 83)( 24, 82)
( 25, 85)( 26, 88)( 27, 87)( 28, 86)( 29, 89)( 30, 92)( 31, 91)( 32, 90)
( 33, 93)( 34, 96)( 35, 95)( 36, 94)( 37, 97)( 38,100)( 39, 99)( 40, 98)
( 41, 61)( 42, 64)( 43, 63)( 44, 62)( 45, 65)( 46, 68)( 47, 67)( 48, 66)
( 49, 69)( 50, 72)( 51, 71)( 52, 70)( 53, 73)( 54, 76)( 55, 75)( 56, 74)
( 57, 77)( 58, 80)( 59, 79)( 60, 78)(121,221)(122,224)(123,223)(124,222)
(125,225)(126,228)(127,227)(128,226)(129,229)(130,232)(131,231)(132,230)
(133,233)(134,236)(135,235)(136,234)(137,237)(138,240)(139,239)(140,238)
(141,201)(142,204)(143,203)(144,202)(145,205)(146,208)(147,207)(148,206)
(149,209)(150,212)(151,211)(152,210)(153,213)(154,216)(155,215)(156,214)
(157,217)(158,220)(159,219)(160,218)(161,181)(162,184)(163,183)(164,182)
(165,185)(166,188)(167,187)(168,186)(169,189)(170,192)(171,191)(172,190)
(173,193)(174,196)(175,195)(176,194)(177,197)(178,200)(179,199)(180,198);;
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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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)!(  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)
( 12, 16)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)
( 32, 36)( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)
( 52, 56)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)
( 72, 76)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)
(112,116)(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)
(132,136)(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)
(152,156)(165,177)(166,178)(167,179)(168,180)(169,173)(170,174)(171,175)
(172,176)(185,197)(186,198)(187,199)(188,200)(189,193)(190,194)(191,195)
(192,196)(205,217)(206,218)(207,219)(208,220)(209,213)(210,214)(211,215)
(212,216)(225,237)(226,238)(227,239)(228,240)(229,233)(230,234)(231,235)
(232,236);
s1 := Sym(240)!(  1,127)(  2,128)(  3,125)(  4,126)(  5,123)(  6,124)(  7,121)
(  8,122)(  9,139)( 10,140)( 11,137)( 12,138)( 13,135)( 14,136)( 15,133)
( 16,134)( 17,131)( 18,132)( 19,129)( 20,130)( 21,147)( 22,148)( 23,145)
( 24,146)( 25,143)( 26,144)( 27,141)( 28,142)( 29,159)( 30,160)( 31,157)
( 32,158)( 33,155)( 34,156)( 35,153)( 36,154)( 37,151)( 38,152)( 39,149)
( 40,150)( 41,167)( 42,168)( 43,165)( 44,166)( 45,163)( 46,164)( 47,161)
( 48,162)( 49,179)( 50,180)( 51,177)( 52,178)( 53,175)( 54,176)( 55,173)
( 56,174)( 57,171)( 58,172)( 59,169)( 60,170)( 61,187)( 62,188)( 63,185)
( 64,186)( 65,183)( 66,184)( 67,181)( 68,182)( 69,199)( 70,200)( 71,197)
( 72,198)( 73,195)( 74,196)( 75,193)( 76,194)( 77,191)( 78,192)( 79,189)
( 80,190)( 81,207)( 82,208)( 83,205)( 84,206)( 85,203)( 86,204)( 87,201)
( 88,202)( 89,219)( 90,220)( 91,217)( 92,218)( 93,215)( 94,216)( 95,213)
( 96,214)( 97,211)( 98,212)( 99,209)(100,210)(101,227)(102,228)(103,225)
(104,226)(105,223)(106,224)(107,221)(108,222)(109,239)(110,240)(111,237)
(112,238)(113,235)(114,236)(115,233)(116,234)(117,231)(118,232)(119,229)
(120,230);
s2 := Sym(240)!(  2,  3)(  6,  7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)
( 23, 42)( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)
( 31, 50)( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)
( 39, 58)( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)
( 82,103)( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)
( 90,111)( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)
( 98,119)( 99,118)(100,120)(122,123)(126,127)(130,131)(134,135)(138,139)
(141,161)(142,163)(143,162)(144,164)(145,165)(146,167)(147,166)(148,168)
(149,169)(150,171)(151,170)(152,172)(153,173)(154,175)(155,174)(156,176)
(157,177)(158,179)(159,178)(160,180)(182,183)(186,187)(190,191)(194,195)
(198,199)(201,221)(202,223)(203,222)(204,224)(205,225)(206,227)(207,226)
(208,228)(209,229)(210,231)(211,230)(212,232)(213,233)(214,235)(215,234)
(216,236)(217,237)(218,239)(219,238)(220,240);
s3 := Sym(240)!(  1,101)(  2,104)(  3,103)(  4,102)(  5,105)(  6,108)(  7,107)
(  8,106)(  9,109)( 10,112)( 11,111)( 12,110)( 13,113)( 14,116)( 15,115)
( 16,114)( 17,117)( 18,120)( 19,119)( 20,118)( 21, 81)( 22, 84)( 23, 83)
( 24, 82)( 25, 85)( 26, 88)( 27, 87)( 28, 86)( 29, 89)( 30, 92)( 31, 91)
( 32, 90)( 33, 93)( 34, 96)( 35, 95)( 36, 94)( 37, 97)( 38,100)( 39, 99)
( 40, 98)( 41, 61)( 42, 64)( 43, 63)( 44, 62)( 45, 65)( 46, 68)( 47, 67)
( 48, 66)( 49, 69)( 50, 72)( 51, 71)( 52, 70)( 53, 73)( 54, 76)( 55, 75)
( 56, 74)( 57, 77)( 58, 80)( 59, 79)( 60, 78)(121,221)(122,224)(123,223)
(124,222)(125,225)(126,228)(127,227)(128,226)(129,229)(130,232)(131,231)
(132,230)(133,233)(134,236)(135,235)(136,234)(137,237)(138,240)(139,239)
(140,238)(141,201)(142,204)(143,203)(144,202)(145,205)(146,208)(147,207)
(148,206)(149,209)(150,212)(151,211)(152,210)(153,213)(154,216)(155,215)
(156,214)(157,217)(158,220)(159,219)(160,218)(161,181)(162,184)(163,183)
(164,182)(165,185)(166,188)(167,187)(168,186)(169,189)(170,192)(171,191)
(172,190)(173,193)(174,196)(175,195)(176,194)(177,197)(178,200)(179,199)
(180,198);
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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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