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