Polytope of Type {10,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8,6}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240213)
Rank : 4
Schlafli Type : {10,8,6}
Number of vertices, edges, etc : 10, 80, 48, 12
Order of s₀s₁s₂s₃ : 30
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 : {10,4,6}*960
   4-fold quotients : {10,4,3}*480
   5-fold quotients : {2,8,6}*384c
   8-fold quotients : {10,2,6}*240
   10-fold quotients : {2,4,6}*192
   16-fold quotients : {5,2,6}*120, {10,2,3}*120
   20-fold quotients : {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   24-fold quotients : {10,2,2}*80
   32-fold quotients : {5,2,3}*60
   40-fold quotients : {2,4,3}*48, {2,2,6}*48
   48-fold quotients : {5,2,2}*40
   80-fold quotients : {2,2,3}*24
   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 := (  1,133)(  2,134)(  3,136)(  4,135)(  5,130)(  6,129)(  7,131)(  8,132)
(  9,125)( 10,126)( 11,128)( 12,127)( 13,122)( 14,121)( 15,123)( 16,124)
( 17,157)( 18,158)( 19,160)( 20,159)( 21,154)( 22,153)( 23,155)( 24,156)
( 25,149)( 26,150)( 27,152)( 28,151)( 29,146)( 30,145)( 31,147)( 32,148)
( 33,141)( 34,142)( 35,144)( 36,143)( 37,138)( 38,137)( 39,139)( 40,140)
( 41,173)( 42,174)( 43,176)( 44,175)( 45,170)( 46,169)( 47,171)( 48,172)
( 49,165)( 50,166)( 51,168)( 52,167)( 53,162)( 54,161)( 55,163)( 56,164)
( 57,197)( 58,198)( 59,200)( 60,199)( 61,194)( 62,193)( 63,195)( 64,196)
( 65,189)( 66,190)( 67,192)( 68,191)( 69,186)( 70,185)( 71,187)( 72,188)
( 73,181)( 74,182)( 75,184)( 76,183)( 77,178)( 78,177)( 79,179)( 80,180)
( 81,213)( 82,214)( 83,216)( 84,215)( 85,210)( 86,209)( 87,211)( 88,212)
( 89,205)( 90,206)( 91,208)( 92,207)( 93,202)( 94,201)( 95,203)( 96,204)
( 97,237)( 98,238)( 99,240)(100,239)(101,234)(102,233)(103,235)(104,236)
(105,229)(106,230)(107,232)(108,231)(109,226)(110,225)(111,227)(112,228)
(113,221)(114,222)(115,224)(116,223)(117,218)(118,217)(119,219)(120,220);;
s2 := (  3,  4)(  5,  7)(  6,  8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)
( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)( 41, 81)
( 42, 82)( 43, 84)( 44, 83)( 45, 87)( 46, 88)( 47, 85)( 48, 86)( 49, 89)
( 50, 90)( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 97)
( 58, 98)( 59,100)( 60, 99)( 61,103)( 62,104)( 63,101)( 64,102)( 65,105)
( 66,106)( 67,108)( 68,107)( 69,111)( 70,112)( 71,109)( 72,110)( 73,113)
( 74,114)( 75,116)( 76,115)( 77,119)( 78,120)( 79,117)( 80,118)(123,124)
(125,127)(126,128)(131,132)(133,135)(134,136)(139,140)(141,143)(142,144)
(147,148)(149,151)(150,152)(155,156)(157,159)(158,160)(161,201)(162,202)
(163,204)(164,203)(165,207)(166,208)(167,205)(168,206)(169,209)(170,210)
(171,212)(172,211)(173,215)(174,216)(175,213)(176,214)(177,217)(178,218)
(179,220)(180,219)(181,223)(182,224)(183,221)(184,222)(185,225)(186,226)
(187,228)(188,227)(189,231)(190,232)(191,229)(192,230)(193,233)(194,234)
(195,236)(196,235)(197,239)(198,240)(199,237)(200,238);;
s3 := (  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)(121,162)
(122,161)(123,168)(124,167)(125,165)(126,166)(127,164)(128,163)(129,170)
(130,169)(131,176)(132,175)(133,173)(134,174)(135,172)(136,171)(137,178)
(138,177)(139,184)(140,183)(141,181)(142,182)(143,180)(144,179)(145,186)
(146,185)(147,192)(148,191)(149,189)(150,190)(151,188)(152,187)(153,194)
(154,193)(155,200)(156,199)(157,197)(158,198)(159,196)(160,195)(201,202)
(203,208)(204,207)(209,210)(211,216)(212,215)(217,218)(219,224)(220,223)
(225,226)(227,232)(228,231)(233,234)(235,240)(236,239);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*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)!(  1,133)(  2,134)(  3,136)(  4,135)(  5,130)(  6,129)(  7,131)
(  8,132)(  9,125)( 10,126)( 11,128)( 12,127)( 13,122)( 14,121)( 15,123)
( 16,124)( 17,157)( 18,158)( 19,160)( 20,159)( 21,154)( 22,153)( 23,155)
( 24,156)( 25,149)( 26,150)( 27,152)( 28,151)( 29,146)( 30,145)( 31,147)
( 32,148)( 33,141)( 34,142)( 35,144)( 36,143)( 37,138)( 38,137)( 39,139)
( 40,140)( 41,173)( 42,174)( 43,176)( 44,175)( 45,170)( 46,169)( 47,171)
( 48,172)( 49,165)( 50,166)( 51,168)( 52,167)( 53,162)( 54,161)( 55,163)
( 56,164)( 57,197)( 58,198)( 59,200)( 60,199)( 61,194)( 62,193)( 63,195)
( 64,196)( 65,189)( 66,190)( 67,192)( 68,191)( 69,186)( 70,185)( 71,187)
( 72,188)( 73,181)( 74,182)( 75,184)( 76,183)( 77,178)( 78,177)( 79,179)
( 80,180)( 81,213)( 82,214)( 83,216)( 84,215)( 85,210)( 86,209)( 87,211)
( 88,212)( 89,205)( 90,206)( 91,208)( 92,207)( 93,202)( 94,201)( 95,203)
( 96,204)( 97,237)( 98,238)( 99,240)(100,239)(101,234)(102,233)(103,235)
(104,236)(105,229)(106,230)(107,232)(108,231)(109,226)(110,225)(111,227)
(112,228)(113,221)(114,222)(115,224)(116,223)(117,218)(118,217)(119,219)
(120,220);
s2 := Sym(240)!(  3,  4)(  5,  7)(  6,  8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)
( 21, 23)( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)
( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 87)( 46, 88)( 47, 85)( 48, 86)
( 49, 89)( 50, 90)( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)
( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61,103)( 62,104)( 63,101)( 64,102)
( 65,105)( 66,106)( 67,108)( 68,107)( 69,111)( 70,112)( 71,109)( 72,110)
( 73,113)( 74,114)( 75,116)( 76,115)( 77,119)( 78,120)( 79,117)( 80,118)
(123,124)(125,127)(126,128)(131,132)(133,135)(134,136)(139,140)(141,143)
(142,144)(147,148)(149,151)(150,152)(155,156)(157,159)(158,160)(161,201)
(162,202)(163,204)(164,203)(165,207)(166,208)(167,205)(168,206)(169,209)
(170,210)(171,212)(172,211)(173,215)(174,216)(175,213)(176,214)(177,217)
(178,218)(179,220)(180,219)(181,223)(182,224)(183,221)(184,222)(185,225)
(186,226)(187,228)(188,227)(189,231)(190,232)(191,229)(192,230)(193,233)
(194,234)(195,236)(196,235)(197,239)(198,240)(199,237)(200,238);
s3 := 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)
(121,162)(122,161)(123,168)(124,167)(125,165)(126,166)(127,164)(128,163)
(129,170)(130,169)(131,176)(132,175)(133,173)(134,174)(135,172)(136,171)
(137,178)(138,177)(139,184)(140,183)(141,181)(142,182)(143,180)(144,179)
(145,186)(146,185)(147,192)(148,191)(149,189)(150,190)(151,188)(152,187)
(153,194)(154,193)(155,200)(156,199)(157,197)(158,198)(159,196)(160,195)
(201,202)(203,208)(204,207)(209,210)(211,216)(212,215)(217,218)(219,224)
(220,223)(225,226)(227,232)(228,231)(233,234)(235,240)(236,239);
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*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