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