Polytope of Type {2,8,10,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,10,5}*1600
if this polytope has a name.
Group : SmallGroup(1600,8648)
Rank : 5
Schlafli Type : {2,8,10,5}
Number of vertices, edges, etc : 2, 8, 40, 25, 5
Order of s0s1s2s3s4 : 40
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
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 : {2,4,10,5}*800
4-fold quotients : {2,2,10,5}*400
5-fold quotients : {2,8,2,5}*320
10-fold quotients : {2,4,2,5}*160
20-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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)
( 51,151)( 52,152)( 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)( 76,201)( 77,202)( 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)(101,176)(102,177);;
s2 := ( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)
( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 53, 78)( 54, 82)( 55, 81)( 56, 80)
( 57, 79)( 58, 83)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 88)( 64, 92)
( 65, 91)( 66, 90)( 67, 89)( 68, 93)( 69, 97)( 70, 96)( 71, 95)( 72, 94)
( 73, 98)( 74,102)( 75,101)( 76,100)( 77, 99)(103,153)(104,157)(105,156)
(106,155)(107,154)(108,158)(109,162)(110,161)(111,160)(112,159)(113,163)
(114,167)(115,166)(116,165)(117,164)(118,168)(119,172)(120,171)(121,170)
(122,169)(123,173)(124,177)(125,176)(126,175)(127,174)(128,178)(129,182)
(130,181)(131,180)(132,179)(133,183)(134,187)(135,186)(136,185)(137,184)
(138,188)(139,192)(140,191)(141,190)(142,189)(143,193)(144,197)(145,196)
(146,195)(147,194)(148,198)(149,202)(150,201)(151,200)(152,199);;
s3 := ( 3, 4)( 5, 7)( 8, 24)( 9, 23)( 10, 27)( 11, 26)( 12, 25)( 13, 19)
( 14, 18)( 15, 22)( 16, 21)( 17, 20)( 28, 29)( 30, 32)( 33, 49)( 34, 48)
( 35, 52)( 36, 51)( 37, 50)( 38, 44)( 39, 43)( 40, 47)( 41, 46)( 42, 45)
( 53, 54)( 55, 57)( 58, 74)( 59, 73)( 60, 77)( 61, 76)( 62, 75)( 63, 69)
( 64, 68)( 65, 72)( 66, 71)( 67, 70)( 78, 79)( 80, 82)( 83, 99)( 84, 98)
( 85,102)( 86,101)( 87,100)( 88, 94)( 89, 93)( 90, 97)( 91, 96)( 92, 95)
(103,104)(105,107)(108,124)(109,123)(110,127)(111,126)(112,125)(113,119)
(114,118)(115,122)(116,121)(117,120)(128,129)(130,132)(133,149)(134,148)
(135,152)(136,151)(137,150)(138,144)(139,143)(140,147)(141,146)(142,145)
(153,154)(155,157)(158,174)(159,173)(160,177)(161,176)(162,175)(163,169)
(164,168)(165,172)(166,171)(167,170)(178,179)(180,182)(183,199)(184,198)
(185,202)(186,201)(187,200)(188,194)(189,193)(190,197)(191,196)(192,195);;
s4 := ( 3, 8)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 13, 23)( 14, 27)( 15, 26)
( 16, 25)( 17, 24)( 19, 22)( 20, 21)( 28, 33)( 29, 37)( 30, 36)( 31, 35)
( 32, 34)( 38, 48)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 44, 47)( 45, 46)
( 53, 58)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 63, 73)( 64, 77)( 65, 76)
( 66, 75)( 67, 74)( 69, 72)( 70, 71)( 78, 83)( 79, 87)( 80, 86)( 81, 85)
( 82, 84)( 88, 98)( 89,102)( 90,101)( 91,100)( 92, 99)( 94, 97)( 95, 96)
(103,108)(104,112)(105,111)(106,110)(107,109)(113,123)(114,127)(115,126)
(116,125)(117,124)(119,122)(120,121)(128,133)(129,137)(130,136)(131,135)
(132,134)(138,148)(139,152)(140,151)(141,150)(142,149)(144,147)(145,146)
(153,158)(154,162)(155,161)(156,160)(157,159)(163,173)(164,177)(165,176)
(166,175)(167,174)(169,172)(170,171)(178,183)(179,187)(180,186)(181,185)
(182,184)(188,198)(189,202)(190,201)(191,200)(192,199)(194,197)(195,196);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(202)!(1,2);
s1 := Sym(202)!( 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)( 51,151)( 52,152)( 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)( 76,201)( 77,202)( 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)(101,176)(102,177);
s2 := Sym(202)!( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)
( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 53, 78)( 54, 82)( 55, 81)
( 56, 80)( 57, 79)( 58, 83)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 88)
( 64, 92)( 65, 91)( 66, 90)( 67, 89)( 68, 93)( 69, 97)( 70, 96)( 71, 95)
( 72, 94)( 73, 98)( 74,102)( 75,101)( 76,100)( 77, 99)(103,153)(104,157)
(105,156)(106,155)(107,154)(108,158)(109,162)(110,161)(111,160)(112,159)
(113,163)(114,167)(115,166)(116,165)(117,164)(118,168)(119,172)(120,171)
(121,170)(122,169)(123,173)(124,177)(125,176)(126,175)(127,174)(128,178)
(129,182)(130,181)(131,180)(132,179)(133,183)(134,187)(135,186)(136,185)
(137,184)(138,188)(139,192)(140,191)(141,190)(142,189)(143,193)(144,197)
(145,196)(146,195)(147,194)(148,198)(149,202)(150,201)(151,200)(152,199);
s3 := Sym(202)!( 3, 4)( 5, 7)( 8, 24)( 9, 23)( 10, 27)( 11, 26)( 12, 25)
( 13, 19)( 14, 18)( 15, 22)( 16, 21)( 17, 20)( 28, 29)( 30, 32)( 33, 49)
( 34, 48)( 35, 52)( 36, 51)( 37, 50)( 38, 44)( 39, 43)( 40, 47)( 41, 46)
( 42, 45)( 53, 54)( 55, 57)( 58, 74)( 59, 73)( 60, 77)( 61, 76)( 62, 75)
( 63, 69)( 64, 68)( 65, 72)( 66, 71)( 67, 70)( 78, 79)( 80, 82)( 83, 99)
( 84, 98)( 85,102)( 86,101)( 87,100)( 88, 94)( 89, 93)( 90, 97)( 91, 96)
( 92, 95)(103,104)(105,107)(108,124)(109,123)(110,127)(111,126)(112,125)
(113,119)(114,118)(115,122)(116,121)(117,120)(128,129)(130,132)(133,149)
(134,148)(135,152)(136,151)(137,150)(138,144)(139,143)(140,147)(141,146)
(142,145)(153,154)(155,157)(158,174)(159,173)(160,177)(161,176)(162,175)
(163,169)(164,168)(165,172)(166,171)(167,170)(178,179)(180,182)(183,199)
(184,198)(185,202)(186,201)(187,200)(188,194)(189,193)(190,197)(191,196)
(192,195);
s4 := Sym(202)!( 3, 8)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 13, 23)( 14, 27)
( 15, 26)( 16, 25)( 17, 24)( 19, 22)( 20, 21)( 28, 33)( 29, 37)( 30, 36)
( 31, 35)( 32, 34)( 38, 48)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 44, 47)
( 45, 46)( 53, 58)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 63, 73)( 64, 77)
( 65, 76)( 66, 75)( 67, 74)( 69, 72)( 70, 71)( 78, 83)( 79, 87)( 80, 86)
( 81, 85)( 82, 84)( 88, 98)( 89,102)( 90,101)( 91,100)( 92, 99)( 94, 97)
( 95, 96)(103,108)(104,112)(105,111)(106,110)(107,109)(113,123)(114,127)
(115,126)(116,125)(117,124)(119,122)(120,121)(128,133)(129,137)(130,136)
(131,135)(132,134)(138,148)(139,152)(140,151)(141,150)(142,149)(144,147)
(145,146)(153,158)(154,162)(155,161)(156,160)(157,159)(163,173)(164,177)
(165,176)(166,175)(167,174)(169,172)(170,171)(178,183)(179,187)(180,186)
(181,185)(182,184)(188,198)(189,202)(190,201)(191,200)(192,199)(194,197)
(195,196);
poly := sub<Sym(202)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope