Polytope of Type {8,4,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,10}*1600
if this polytope has a name.
Group : SmallGroup(1600,6672)
Rank : 4
Schlafli Type : {8,4,10}
Number of vertices, edges, etc : 8, 40, 50, 25
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-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 : {4,4,10}*800
4-fold quotients : {2,4,10}*400
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,101)( 2,102)( 3,103)( 4,104)( 5,105)( 6,106)( 7,107)( 8,108)
( 9,109)( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)( 16,116)
( 17,117)( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)( 24,124)
( 25,125)( 26,126)( 27,127)( 28,128)( 29,129)( 30,130)( 31,131)( 32,132)
( 33,133)( 34,134)( 35,135)( 36,136)( 37,137)( 38,138)( 39,139)( 40,140)
( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)( 48,148)
( 49,149)( 50,150)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)( 56,181)
( 57,182)( 58,183)( 59,184)( 60,185)( 61,186)( 62,187)( 63,188)( 64,189)
( 65,190)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,196)( 72,197)
( 73,198)( 74,199)( 75,200)( 76,151)( 77,152)( 78,153)( 79,154)( 80,155)
( 81,156)( 82,157)( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)( 88,163)
( 89,164)( 90,165)( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)( 96,171)
( 97,172)( 98,173)( 99,174)(100,175);;
s1 := ( 2, 9)( 3, 12)( 4, 20)( 5, 23)( 6, 13)( 7, 16)( 8, 24)( 11, 25)
( 15, 17)( 19, 21)( 27, 34)( 28, 37)( 29, 45)( 30, 48)( 31, 38)( 32, 41)
( 33, 49)( 36, 50)( 40, 42)( 44, 46)( 51, 76)( 52, 84)( 53, 87)( 54, 95)
( 55, 98)( 56, 88)( 57, 91)( 58, 99)( 59, 77)( 60, 85)( 61,100)( 62, 78)
( 63, 81)( 64, 89)( 65, 92)( 66, 82)( 67, 90)( 68, 93)( 69, 96)( 70, 79)
( 71, 94)( 72, 97)( 73, 80)( 74, 83)( 75, 86)(101,151)(102,159)(103,162)
(104,170)(105,173)(106,163)(107,166)(108,174)(109,152)(110,160)(111,175)
(112,153)(113,156)(114,164)(115,167)(116,157)(117,165)(118,168)(119,171)
(120,154)(121,169)(122,172)(123,155)(124,158)(125,161)(126,176)(127,184)
(128,187)(129,195)(130,198)(131,188)(132,191)(133,199)(134,177)(135,185)
(136,200)(137,178)(138,181)(139,189)(140,192)(141,182)(142,190)(143,193)
(144,196)(145,179)(146,194)(147,197)(148,180)(149,183)(150,186);;
s2 := ( 2, 12)( 3, 23)( 4, 9)( 5, 20)( 6, 21)( 8, 18)( 10, 15)( 11, 16)
( 14, 24)( 17, 22)( 27, 37)( 28, 48)( 29, 34)( 30, 45)( 31, 46)( 33, 43)
( 35, 40)( 36, 41)( 39, 49)( 42, 47)( 52, 62)( 53, 73)( 54, 59)( 55, 70)
( 56, 71)( 58, 68)( 60, 65)( 61, 66)( 64, 74)( 67, 72)( 77, 87)( 78, 98)
( 79, 84)( 80, 95)( 81, 96)( 83, 93)( 85, 90)( 86, 91)( 89, 99)( 92, 97)
(102,112)(103,123)(104,109)(105,120)(106,121)(108,118)(110,115)(111,116)
(114,124)(117,122)(127,137)(128,148)(129,134)(130,145)(131,146)(133,143)
(135,140)(136,141)(139,149)(142,147)(152,162)(153,173)(154,159)(155,170)
(156,171)(158,168)(160,165)(161,166)(164,174)(167,172)(177,187)(178,198)
(179,184)(180,195)(181,196)(183,193)(185,190)(186,191)(189,199)(192,197);;
s3 := ( 1, 22)( 2, 21)( 3, 25)( 4, 24)( 5, 23)( 6, 17)( 7, 16)( 8, 20)
( 9, 19)( 10, 18)( 11, 12)( 13, 15)( 26, 47)( 27, 46)( 28, 50)( 29, 49)
( 30, 48)( 31, 42)( 32, 41)( 33, 45)( 34, 44)( 35, 43)( 36, 37)( 38, 40)
( 51, 72)( 52, 71)( 53, 75)( 54, 74)( 55, 73)( 56, 67)( 57, 66)( 58, 70)
( 59, 69)( 60, 68)( 61, 62)( 63, 65)( 76, 97)( 77, 96)( 78,100)( 79, 99)
( 80, 98)( 81, 92)( 82, 91)( 83, 95)( 84, 94)( 85, 93)( 86, 87)( 88, 90)
(101,122)(102,121)(103,125)(104,124)(105,123)(106,117)(107,116)(108,120)
(109,119)(110,118)(111,112)(113,115)(126,147)(127,146)(128,150)(129,149)
(130,148)(131,142)(132,141)(133,145)(134,144)(135,143)(136,137)(138,140)
(151,172)(152,171)(153,175)(154,174)(155,173)(156,167)(157,166)(158,170)
(159,169)(160,168)(161,162)(163,165)(176,197)(177,196)(178,200)(179,199)
(180,198)(181,192)(182,191)(183,195)(184,194)(185,193)(186,187)(188,190);;
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, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(200)!( 1,101)( 2,102)( 3,103)( 4,104)( 5,105)( 6,106)( 7,107)
( 8,108)( 9,109)( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)
( 16,116)( 17,117)( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)
( 24,124)( 25,125)( 26,126)( 27,127)( 28,128)( 29,129)( 30,130)( 31,131)
( 32,132)( 33,133)( 34,134)( 35,135)( 36,136)( 37,137)( 38,138)( 39,139)
( 40,140)( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)
( 48,148)( 49,149)( 50,150)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)
( 56,181)( 57,182)( 58,183)( 59,184)( 60,185)( 61,186)( 62,187)( 63,188)
( 64,189)( 65,190)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,196)
( 72,197)( 73,198)( 74,199)( 75,200)( 76,151)( 77,152)( 78,153)( 79,154)
( 80,155)( 81,156)( 82,157)( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)
( 88,163)( 89,164)( 90,165)( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)
( 96,171)( 97,172)( 98,173)( 99,174)(100,175);
s1 := Sym(200)!( 2, 9)( 3, 12)( 4, 20)( 5, 23)( 6, 13)( 7, 16)( 8, 24)
( 11, 25)( 15, 17)( 19, 21)( 27, 34)( 28, 37)( 29, 45)( 30, 48)( 31, 38)
( 32, 41)( 33, 49)( 36, 50)( 40, 42)( 44, 46)( 51, 76)( 52, 84)( 53, 87)
( 54, 95)( 55, 98)( 56, 88)( 57, 91)( 58, 99)( 59, 77)( 60, 85)( 61,100)
( 62, 78)( 63, 81)( 64, 89)( 65, 92)( 66, 82)( 67, 90)( 68, 93)( 69, 96)
( 70, 79)( 71, 94)( 72, 97)( 73, 80)( 74, 83)( 75, 86)(101,151)(102,159)
(103,162)(104,170)(105,173)(106,163)(107,166)(108,174)(109,152)(110,160)
(111,175)(112,153)(113,156)(114,164)(115,167)(116,157)(117,165)(118,168)
(119,171)(120,154)(121,169)(122,172)(123,155)(124,158)(125,161)(126,176)
(127,184)(128,187)(129,195)(130,198)(131,188)(132,191)(133,199)(134,177)
(135,185)(136,200)(137,178)(138,181)(139,189)(140,192)(141,182)(142,190)
(143,193)(144,196)(145,179)(146,194)(147,197)(148,180)(149,183)(150,186);
s2 := Sym(200)!( 2, 12)( 3, 23)( 4, 9)( 5, 20)( 6, 21)( 8, 18)( 10, 15)
( 11, 16)( 14, 24)( 17, 22)( 27, 37)( 28, 48)( 29, 34)( 30, 45)( 31, 46)
( 33, 43)( 35, 40)( 36, 41)( 39, 49)( 42, 47)( 52, 62)( 53, 73)( 54, 59)
( 55, 70)( 56, 71)( 58, 68)( 60, 65)( 61, 66)( 64, 74)( 67, 72)( 77, 87)
( 78, 98)( 79, 84)( 80, 95)( 81, 96)( 83, 93)( 85, 90)( 86, 91)( 89, 99)
( 92, 97)(102,112)(103,123)(104,109)(105,120)(106,121)(108,118)(110,115)
(111,116)(114,124)(117,122)(127,137)(128,148)(129,134)(130,145)(131,146)
(133,143)(135,140)(136,141)(139,149)(142,147)(152,162)(153,173)(154,159)
(155,170)(156,171)(158,168)(160,165)(161,166)(164,174)(167,172)(177,187)
(178,198)(179,184)(180,195)(181,196)(183,193)(185,190)(186,191)(189,199)
(192,197);
s3 := Sym(200)!( 1, 22)( 2, 21)( 3, 25)( 4, 24)( 5, 23)( 6, 17)( 7, 16)
( 8, 20)( 9, 19)( 10, 18)( 11, 12)( 13, 15)( 26, 47)( 27, 46)( 28, 50)
( 29, 49)( 30, 48)( 31, 42)( 32, 41)( 33, 45)( 34, 44)( 35, 43)( 36, 37)
( 38, 40)( 51, 72)( 52, 71)( 53, 75)( 54, 74)( 55, 73)( 56, 67)( 57, 66)
( 58, 70)( 59, 69)( 60, 68)( 61, 62)( 63, 65)( 76, 97)( 77, 96)( 78,100)
( 79, 99)( 80, 98)( 81, 92)( 82, 91)( 83, 95)( 84, 94)( 85, 93)( 86, 87)
( 88, 90)(101,122)(102,121)(103,125)(104,124)(105,123)(106,117)(107,116)
(108,120)(109,119)(110,118)(111,112)(113,115)(126,147)(127,146)(128,150)
(129,149)(130,148)(131,142)(132,141)(133,145)(134,144)(135,143)(136,137)
(138,140)(151,172)(152,171)(153,175)(154,174)(155,173)(156,167)(157,166)
(158,170)(159,169)(160,168)(161,162)(163,165)(176,197)(177,196)(178,200)
(179,199)(180,198)(181,192)(182,191)(183,195)(184,194)(185,193)(186,187)
(188,190);
poly := sub<Sym(200)|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,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2 >;
References : None.
to this polytope