Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,40,10}

Atlas Canonical Name {2,40,10}*1600a

Overview

Group
SmallGroup(1600,8115)
Rank
4
Schläfli Type
{2,40,10}
Vertices, edges, …
2, 40, 200, 10
Order of s0s1s2s3
40
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

5-fold

10-fold

20-fold

25-fold

40-fold

50-fold

100-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (  8, 23)(  9, 24)( 10, 25)( 11, 26)( 12, 27)( 13, 18)( 14, 19)( 15, 20)( 16, 21)( 17, 22)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 53, 78)( 54, 79)( 55, 80)( 56, 81)( 57, 82)( 58, 98)( 59, 99)( 60,100)( 61,101)( 62,102)( 63, 93)( 64, 94)( 65, 95)( 66, 96)( 67, 97)( 68, 88)( 69, 89)( 70, 90)( 71, 91)( 72, 92)( 73, 83)( 74, 84)( 75, 85)( 76, 86)( 77, 87)(103,153)(104,154)(105,155)(106,156)(107,157)(108,173)(109,174)(110,175)(111,176)(112,177)(113,168)(114,169)(115,170)(116,171)(117,172)(118,163)(119,164)(120,165)(121,166)(122,167)(123,158)(124,159)(125,160)(126,161)(127,162)(128,178)(129,179)(130,180)(131,181)(132,182)(133,198)(134,199)(135,200)(136,201)(137,202)(138,193)(139,194)(140,195)(141,196)(142,197)(143,188)(144,189)(145,190)(146,191)(147,192)(148,183)(149,184)(150,185)(151,186)(152,187);;
s2 := (  3,108)(  4,112)(  5,111)(  6,110)(  7,109)(  8,103)(  9,107)( 10,106)( 11,105)( 12,104)( 13,123)( 14,127)( 15,126)( 16,125)( 17,124)( 18,118)( 19,122)( 20,121)( 21,120)( 22,119)( 23,113)( 24,117)( 25,116)( 26,115)( 27,114)( 28,133)( 29,137)( 30,136)( 31,135)( 32,134)( 33,128)( 34,132)( 35,131)( 36,130)( 37,129)( 38,148)( 39,152)( 40,151)( 41,150)( 42,149)( 43,143)( 44,147)( 45,146)( 46,145)( 47,144)( 48,138)( 49,142)( 50,141)( 51,140)( 52,139)( 53,183)( 54,187)( 55,186)( 56,185)( 57,184)( 58,178)( 59,182)( 60,181)( 61,180)( 62,179)( 63,198)( 64,202)( 65,201)( 66,200)( 67,199)( 68,193)( 69,197)( 70,196)( 71,195)( 72,194)( 73,188)( 74,192)( 75,191)( 76,190)( 77,189)( 78,158)( 79,162)( 80,161)( 81,160)( 82,159)( 83,153)( 84,157)( 85,156)( 86,155)( 87,154)( 88,173)( 89,177)( 90,176)( 91,175)( 92,174)( 93,168)( 94,172)( 95,171)( 96,170)( 97,169)( 98,163)( 99,167)(100,166)(101,165)(102,164);;
s3 := (  3,  4)(  5,  7)(  8,  9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)( 20, 22)( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)( 40, 42)( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)( 60, 62)( 63, 64)( 65, 67)( 68, 69)( 70, 72)( 73, 74)( 75, 77)( 78, 79)( 80, 82)( 83, 84)( 85, 87)( 88, 89)( 90, 92)( 93, 94)( 95, 97)( 98, 99)(100,102)(103,104)(105,107)(108,109)(110,112)(113,114)(115,117)(118,119)(120,122)(123,124)(125,127)(128,129)(130,132)(133,134)(135,137)(138,139)(140,142)(143,144)(145,147)(148,149)(150,152)(153,154)(155,157)(158,159)(160,162)(163,164)(165,167)(168,169)(170,172)(173,174)(175,177)(178,179)(180,182)(183,184)(185,187)(188,189)(190,192)(193,194)(195,197)(198,199)(200,202);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)!(  8, 23)(  9, 24)( 10, 25)( 11, 26)( 12, 27)( 13, 18)( 14, 19)( 15, 20)( 16, 21)( 17, 22)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 53, 78)( 54, 79)( 55, 80)( 56, 81)( 57, 82)( 58, 98)( 59, 99)( 60,100)( 61,101)( 62,102)( 63, 93)( 64, 94)( 65, 95)( 66, 96)( 67, 97)( 68, 88)( 69, 89)( 70, 90)( 71, 91)( 72, 92)( 73, 83)( 74, 84)( 75, 85)( 76, 86)( 77, 87)(103,153)(104,154)(105,155)(106,156)(107,157)(108,173)(109,174)(110,175)(111,176)(112,177)(113,168)(114,169)(115,170)(116,171)(117,172)(118,163)(119,164)(120,165)(121,166)(122,167)(123,158)(124,159)(125,160)(126,161)(127,162)(128,178)(129,179)(130,180)(131,181)(132,182)(133,198)(134,199)(135,200)(136,201)(137,202)(138,193)(139,194)(140,195)(141,196)(142,197)(143,188)(144,189)(145,190)(146,191)(147,192)(148,183)(149,184)(150,185)(151,186)(152,187);
s2 := Sym(202)!(  3,108)(  4,112)(  5,111)(  6,110)(  7,109)(  8,103)(  9,107)( 10,106)( 11,105)( 12,104)( 13,123)( 14,127)( 15,126)( 16,125)( 17,124)( 18,118)( 19,122)( 20,121)( 21,120)( 22,119)( 23,113)( 24,117)( 25,116)( 26,115)( 27,114)( 28,133)( 29,137)( 30,136)( 31,135)( 32,134)( 33,128)( 34,132)( 35,131)( 36,130)( 37,129)( 38,148)( 39,152)( 40,151)( 41,150)( 42,149)( 43,143)( 44,147)( 45,146)( 46,145)( 47,144)( 48,138)( 49,142)( 50,141)( 51,140)( 52,139)( 53,183)( 54,187)( 55,186)( 56,185)( 57,184)( 58,178)( 59,182)( 60,181)( 61,180)( 62,179)( 63,198)( 64,202)( 65,201)( 66,200)( 67,199)( 68,193)( 69,197)( 70,196)( 71,195)( 72,194)( 73,188)( 74,192)( 75,191)( 76,190)( 77,189)( 78,158)( 79,162)( 80,161)( 81,160)( 82,159)( 83,153)( 84,157)( 85,156)( 86,155)( 87,154)( 88,173)( 89,177)( 90,176)( 91,175)( 92,174)( 93,168)( 94,172)( 95,171)( 96,170)( 97,169)( 98,163)( 99,167)(100,166)(101,165)(102,164);
s3 := Sym(202)!(  3,  4)(  5,  7)(  8,  9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)( 20, 22)( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)( 40, 42)( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)( 60, 62)( 63, 64)( 65, 67)( 68, 69)( 70, 72)( 73, 74)( 75, 77)( 78, 79)( 80, 82)( 83, 84)( 85, 87)( 88, 89)( 90, 92)( 93, 94)( 95, 97)( 98, 99)(100,102)(103,104)(105,107)(108,109)(110,112)(113,114)(115,117)(118,119)(120,122)(123,124)(125,127)(128,129)(130,132)(133,134)(135,137)(138,139)(140,142)(143,144)(145,147)(148,149)(150,152)(153,154)(155,157)(158,159)(160,162)(163,164)(165,167)(168,169)(170,172)(173,174)(175,177)(178,179)(180,182)(183,184)(185,187)(188,189)(190,192)(193,194)(195,197)(198,199)(200,202);
poly := sub<Sym(202)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;