Polytope of Type {6,8,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,10}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240213)
Rank : 4
Schlafli Type : {6,8,10}
Number of vertices, edges, etc : 12, 48, 80, 10
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 : {6,4,10}*960
   4-fold quotients : {3,4,10}*480
   5-fold quotients : {6,8,2}*384c
   8-fold quotients : {6,2,10}*240
   10-fold quotients : {6,4,2}*192
   16-fold quotients : {3,2,10}*120, {6,2,5}*120
   20-fold quotients : {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   24-fold quotients : {2,2,10}*80
   32-fold quotients : {3,2,5}*60
   40-fold quotients : {3,4,2}*48, {6,2,2}*48
   48-fold quotients : {2,2,5}*40
   80-fold quotients : {3,2,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope