Polytope of Type {8,10,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,10,10}*1600b
if this polytope has a name.
Group : SmallGroup(1600,8167)
Rank : 4
Schlafli Type : {8,10,10}
Number of vertices, edges, etc : 8, 40, 50, 10
Order of s0s1s2s3 : 40
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 : {4,10,10}*800b
4-fold quotients : {2,10,10}*400c
5-fold quotients : {8,10,2}*320
8-fold quotients : {2,5,10}*200
10-fold quotients : {4,10,2}*160
20-fold quotients : {2,10,2}*80
25-fold quotients : {8,2,2}*64
40-fold quotients : {2,5,2}*40
50-fold quotients : {4,2,2}*32
100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)( 56, 81)( 57, 82)( 58, 83)
( 59, 84)( 60, 85)( 61, 86)( 62, 87)( 63, 88)( 64, 89)( 65, 90)( 66, 91)
( 67, 92)( 68, 93)( 69, 94)( 70, 95)( 71, 96)( 72, 97)( 73, 98)( 74, 99)
( 75,100)(101,151)(102,152)(103,153)(104,154)(105,155)(106,156)(107,157)
(108,158)(109,159)(110,160)(111,161)(112,162)(113,163)(114,164)(115,165)
(116,166)(117,167)(118,168)(119,169)(120,170)(121,171)(122,172)(123,173)
(124,174)(125,175)(126,176)(127,177)(128,178)(129,179)(130,180)(131,181)
(132,182)(133,183)(134,184)(135,185)(136,186)(137,187)(138,188)(139,189)
(140,190)(141,191)(142,192)(143,193)(144,194)(145,195)(146,196)(147,197)
(148,198)(149,199)(150,200);;
s1 := ( 1,101)( 2,105)( 3,104)( 4,103)( 5,102)( 6,121)( 7,125)( 8,124)
( 9,123)( 10,122)( 11,116)( 12,120)( 13,119)( 14,118)( 15,117)( 16,111)
( 17,115)( 18,114)( 19,113)( 20,112)( 21,106)( 22,110)( 23,109)( 24,108)
( 25,107)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,146)( 32,150)
( 33,149)( 34,148)( 35,147)( 36,141)( 37,145)( 38,144)( 39,143)( 40,142)
( 41,136)( 42,140)( 43,139)( 44,138)( 45,137)( 46,131)( 47,135)( 48,134)
( 49,133)( 50,132)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)( 56,196)
( 57,200)( 58,199)( 59,198)( 60,197)( 61,191)( 62,195)( 63,194)( 64,193)
( 65,192)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,181)( 72,185)
( 73,184)( 74,183)( 75,182)( 76,151)( 77,155)( 78,154)( 79,153)( 80,152)
( 81,171)( 82,175)( 83,174)( 84,173)( 85,172)( 86,166)( 87,170)( 88,169)
( 89,168)( 90,167)( 91,161)( 92,165)( 93,164)( 94,163)( 95,162)( 96,156)
( 97,160)( 98,159)( 99,158)(100,157);;
s2 := ( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 22)( 12, 21)( 13, 25)
( 14, 24)( 15, 23)( 16, 17)( 18, 20)( 26, 32)( 27, 31)( 28, 35)( 29, 34)
( 30, 33)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)( 41, 42)( 43, 45)
( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 72)( 62, 71)( 63, 75)
( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76, 82)( 77, 81)( 78, 85)( 79, 84)
( 80, 83)( 86, 97)( 87, 96)( 88,100)( 89, 99)( 90, 98)( 91, 92)( 93, 95)
(101,107)(102,106)(103,110)(104,109)(105,108)(111,122)(112,121)(113,125)
(114,124)(115,123)(116,117)(118,120)(126,132)(127,131)(128,135)(129,134)
(130,133)(136,147)(137,146)(138,150)(139,149)(140,148)(141,142)(143,145)
(151,157)(152,156)(153,160)(154,159)(155,158)(161,172)(162,171)(163,175)
(164,174)(165,173)(166,167)(168,170)(176,182)(177,181)(178,185)(179,184)
(180,183)(186,197)(187,196)(188,200)(189,199)(190,198)(191,192)(193,195);;
s3 := ( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)
( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)( 59, 74)
( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)( 82, 97)
( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)
(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)
(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)
(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)(159,174)
(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)(182,197)
(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)(190,195);;
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,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(200)!( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)( 56, 81)( 57, 82)
( 58, 83)( 59, 84)( 60, 85)( 61, 86)( 62, 87)( 63, 88)( 64, 89)( 65, 90)
( 66, 91)( 67, 92)( 68, 93)( 69, 94)( 70, 95)( 71, 96)( 72, 97)( 73, 98)
( 74, 99)( 75,100)(101,151)(102,152)(103,153)(104,154)(105,155)(106,156)
(107,157)(108,158)(109,159)(110,160)(111,161)(112,162)(113,163)(114,164)
(115,165)(116,166)(117,167)(118,168)(119,169)(120,170)(121,171)(122,172)
(123,173)(124,174)(125,175)(126,176)(127,177)(128,178)(129,179)(130,180)
(131,181)(132,182)(133,183)(134,184)(135,185)(136,186)(137,187)(138,188)
(139,189)(140,190)(141,191)(142,192)(143,193)(144,194)(145,195)(146,196)
(147,197)(148,198)(149,199)(150,200);
s1 := Sym(200)!( 1,101)( 2,105)( 3,104)( 4,103)( 5,102)( 6,121)( 7,125)
( 8,124)( 9,123)( 10,122)( 11,116)( 12,120)( 13,119)( 14,118)( 15,117)
( 16,111)( 17,115)( 18,114)( 19,113)( 20,112)( 21,106)( 22,110)( 23,109)
( 24,108)( 25,107)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,146)
( 32,150)( 33,149)( 34,148)( 35,147)( 36,141)( 37,145)( 38,144)( 39,143)
( 40,142)( 41,136)( 42,140)( 43,139)( 44,138)( 45,137)( 46,131)( 47,135)
( 48,134)( 49,133)( 50,132)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)
( 56,196)( 57,200)( 58,199)( 59,198)( 60,197)( 61,191)( 62,195)( 63,194)
( 64,193)( 65,192)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,181)
( 72,185)( 73,184)( 74,183)( 75,182)( 76,151)( 77,155)( 78,154)( 79,153)
( 80,152)( 81,171)( 82,175)( 83,174)( 84,173)( 85,172)( 86,166)( 87,170)
( 88,169)( 89,168)( 90,167)( 91,161)( 92,165)( 93,164)( 94,163)( 95,162)
( 96,156)( 97,160)( 98,159)( 99,158)(100,157);
s2 := Sym(200)!( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 22)( 12, 21)
( 13, 25)( 14, 24)( 15, 23)( 16, 17)( 18, 20)( 26, 32)( 27, 31)( 28, 35)
( 29, 34)( 30, 33)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)( 41, 42)
( 43, 45)( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 72)( 62, 71)
( 63, 75)( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76, 82)( 77, 81)( 78, 85)
( 79, 84)( 80, 83)( 86, 97)( 87, 96)( 88,100)( 89, 99)( 90, 98)( 91, 92)
( 93, 95)(101,107)(102,106)(103,110)(104,109)(105,108)(111,122)(112,121)
(113,125)(114,124)(115,123)(116,117)(118,120)(126,132)(127,131)(128,135)
(129,134)(130,133)(136,147)(137,146)(138,150)(139,149)(140,148)(141,142)
(143,145)(151,157)(152,156)(153,160)(154,159)(155,158)(161,172)(162,171)
(163,175)(164,174)(165,173)(166,167)(168,170)(176,182)(177,181)(178,185)
(179,184)(180,183)(186,197)(187,196)(188,200)(189,199)(190,198)(191,192)
(193,195);
s3 := Sym(200)!( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)
( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)
( 59, 74)( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)
( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)
( 90, 95)(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)
(113,118)(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)
(136,141)(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)
(159,174)(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)
(182,197)(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)
(190,195);
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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope