Overview
- Group
- SmallGroup(1600,8514)
- Rank
- 4
- Schläfli Type
- {2,20,20}
- Vertices, edges, …
- 2, 20, 200, 20
- Order of s0s1s2s3
- 20
- 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)( 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)(103,178)(104,182)(105,181)(106,180)(107,179)(108,198)(109,202)(110,201)(111,200)(112,199)(113,193)(114,197)(115,196)(116,195)(117,194)(118,188)(119,192)(120,191)(121,190)(122,189)(123,183)(124,187)(125,186)(126,185)(127,184)(128,153)(129,157)(130,156)(131,155)(132,154)(133,173)(134,177)(135,176)(136,175)(137,174)(138,168)(139,172)(140,171)(141,170)(142,169)(143,163)(144,167)(145,166)(146,165)(147,164)(148,158)(149,162)(150,161)(151,160)(152,159);; 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)( 53,159)( 54,158)( 55,162)( 56,161)( 57,160)( 58,154)( 59,153)( 60,157)( 61,156)( 62,155)( 63,174)( 64,173)( 65,177)( 66,176)( 67,175)( 68,169)( 69,168)( 70,172)( 71,171)( 72,170)( 73,164)( 74,163)( 75,167)( 76,166)( 77,165)( 78,184)( 79,183)( 80,187)( 81,186)( 82,185)( 83,179)( 84,178)( 85,182)( 86,181)( 87,180)( 88,199)( 89,198)( 90,202)( 91,201)( 92,200)( 93,194)( 94,193)( 95,197)( 96,196)( 97,195)( 98,189)( 99,188)(100,192)(101,191)(102,190);; 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)(103,128)(104,132)(105,131)(106,130)(107,129)(108,133)(109,137)(110,136)(111,135)(112,134)(113,138)(114,142)(115,141)(116,140)(117,139)(118,143)(119,147)(120,146)(121,145)(122,144)(123,148)(124,152)(125,151)(126,150)(127,149)(153,178)(154,182)(155,181)(156,180)(157,179)(158,183)(159,187)(160,186)(161,185)(162,184)(163,188)(164,192)(165,191)(166,190)(167,189)(168,193)(169,197)(170,196)(171,195)(172,194)(173,198)(174,202)(175,201)(176,200)(177,199);; 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*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*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)( 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)(103,178)(104,182)(105,181)(106,180)(107,179)(108,198)(109,202)(110,201)(111,200)(112,199)(113,193)(114,197)(115,196)(116,195)(117,194)(118,188)(119,192)(120,191)(121,190)(122,189)(123,183)(124,187)(125,186)(126,185)(127,184)(128,153)(129,157)(130,156)(131,155)(132,154)(133,173)(134,177)(135,176)(136,175)(137,174)(138,168)(139,172)(140,171)(141,170)(142,169)(143,163)(144,167)(145,166)(146,165)(147,164)(148,158)(149,162)(150,161)(151,160)(152,159); 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)( 53,159)( 54,158)( 55,162)( 56,161)( 57,160)( 58,154)( 59,153)( 60,157)( 61,156)( 62,155)( 63,174)( 64,173)( 65,177)( 66,176)( 67,175)( 68,169)( 69,168)( 70,172)( 71,171)( 72,170)( 73,164)( 74,163)( 75,167)( 76,166)( 77,165)( 78,184)( 79,183)( 80,187)( 81,186)( 82,185)( 83,179)( 84,178)( 85,182)( 86,181)( 87,180)( 88,199)( 89,198)( 90,202)( 91,201)( 92,200)( 93,194)( 94,193)( 95,197)( 96,196)( 97,195)( 98,189)( 99,188)(100,192)(101,191)(102,190); 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)(103,128)(104,132)(105,131)(106,130)(107,129)(108,133)(109,137)(110,136)(111,135)(112,134)(113,138)(114,142)(115,141)(116,140)(117,139)(118,143)(119,147)(120,146)(121,145)(122,144)(123,148)(124,152)(125,151)(126,150)(127,149)(153,178)(154,182)(155,181)(156,180)(157,179)(158,183)(159,187)(160,186)(161,185)(162,184)(163,188)(164,192)(165,191)(166,190)(167,189)(168,193)(169,197)(170,196)(171,195)(172,194)(173,198)(174,202)(175,201)(176,200)(177,199); 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*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2 >;