Polytope of Type {8,6,10}

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

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