Overview
- Group
- SmallGroup(1600,1163)
- Rank
- 4
- Schläfli Type
- {4,100,2}
- Vertices, edges, …
- 4, 200, 100, 2
- Order of s0s1s2s3
- 100
- 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 := (101,126)(102,127)(103,128)(104,129)(105,130)(106,131)(107,132)(108,133)(109,134)(110,135)(111,136)(112,137)(113,138)(114,139)(115,140)(116,141)(117,142)(118,143)(119,144)(120,145)(121,146)(122,147)(123,148)(124,149)(125,150)(151,176)(152,177)(153,178)(154,179)(155,180)(156,181)(157,182)(158,183)(159,184)(160,185)(161,186)(162,187)(163,188)(164,189)(165,190)(166,191)(167,192)(168,193)(169,194)(170,195)(171,196)(172,197)(173,198)(174,199)(175,200);; s1 := ( 1,101)( 2,105)( 3,104)( 4,103)( 5,102)( 6,125)( 7,124)( 8,123)( 9,122)( 10,121)( 11,120)( 12,119)( 13,118)( 14,117)( 15,116)( 16,115)( 17,114)( 18,113)( 19,112)( 20,111)( 21,110)( 22,109)( 23,108)( 24,107)( 25,106)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,150)( 32,149)( 33,148)( 34,147)( 35,146)( 36,145)( 37,144)( 38,143)( 39,142)( 40,141)( 41,140)( 42,139)( 43,138)( 44,137)( 45,136)( 46,135)( 47,134)( 48,133)( 49,132)( 50,131)( 51,151)( 52,155)( 53,154)( 54,153)( 55,152)( 56,175)( 57,174)( 58,173)( 59,172)( 60,171)( 61,170)( 62,169)( 63,168)( 64,167)( 65,166)( 66,165)( 67,164)( 68,163)( 69,162)( 70,161)( 71,160)( 72,159)( 73,158)( 74,157)( 75,156)( 76,176)( 77,180)( 78,179)( 79,178)( 80,177)( 81,200)( 82,199)( 83,198)( 84,197)( 85,196)( 86,195)( 87,194)( 88,193)( 89,192)( 90,191)( 91,190)( 92,189)( 93,188)( 94,187)( 95,186)( 96,185)( 97,184)( 98,183)( 99,182)(100,181);; s2 := ( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 26, 31)( 27, 35)( 28, 34)( 29, 33)( 30, 32)( 36, 50)( 37, 49)( 38, 48)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 75)( 62, 74)( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 76, 81)( 77, 85)( 78, 84)( 79, 83)( 80, 82)( 86,100)( 87, 99)( 88, 98)( 89, 97)( 90, 96)( 91, 95)( 92, 94)(101,156)(102,160)(103,159)(104,158)(105,157)(106,151)(107,155)(108,154)(109,153)(110,152)(111,175)(112,174)(113,173)(114,172)(115,171)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)(122,164)(123,163)(124,162)(125,161)(126,181)(127,185)(128,184)(129,183)(130,182)(131,176)(132,180)(133,179)(134,178)(135,177)(136,200)(137,199)(138,198)(139,197)(140,196)(141,195)(142,194)(143,193)(144,192)(145,191)(146,190)(147,189)(148,188)(149,187)(150,186);; s3 := (201,202);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
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*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*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)!(101,126)(102,127)(103,128)(104,129)(105,130)(106,131)(107,132)(108,133)(109,134)(110,135)(111,136)(112,137)(113,138)(114,139)(115,140)(116,141)(117,142)(118,143)(119,144)(120,145)(121,146)(122,147)(123,148)(124,149)(125,150)(151,176)(152,177)(153,178)(154,179)(155,180)(156,181)(157,182)(158,183)(159,184)(160,185)(161,186)(162,187)(163,188)(164,189)(165,190)(166,191)(167,192)(168,193)(169,194)(170,195)(171,196)(172,197)(173,198)(174,199)(175,200); s1 := Sym(202)!( 1,101)( 2,105)( 3,104)( 4,103)( 5,102)( 6,125)( 7,124)( 8,123)( 9,122)( 10,121)( 11,120)( 12,119)( 13,118)( 14,117)( 15,116)( 16,115)( 17,114)( 18,113)( 19,112)( 20,111)( 21,110)( 22,109)( 23,108)( 24,107)( 25,106)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,150)( 32,149)( 33,148)( 34,147)( 35,146)( 36,145)( 37,144)( 38,143)( 39,142)( 40,141)( 41,140)( 42,139)( 43,138)( 44,137)( 45,136)( 46,135)( 47,134)( 48,133)( 49,132)( 50,131)( 51,151)( 52,155)( 53,154)( 54,153)( 55,152)( 56,175)( 57,174)( 58,173)( 59,172)( 60,171)( 61,170)( 62,169)( 63,168)( 64,167)( 65,166)( 66,165)( 67,164)( 68,163)( 69,162)( 70,161)( 71,160)( 72,159)( 73,158)( 74,157)( 75,156)( 76,176)( 77,180)( 78,179)( 79,178)( 80,177)( 81,200)( 82,199)( 83,198)( 84,197)( 85,196)( 86,195)( 87,194)( 88,193)( 89,192)( 90,191)( 91,190)( 92,189)( 93,188)( 94,187)( 95,186)( 96,185)( 97,184)( 98,183)( 99,182)(100,181); s2 := Sym(202)!( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 26, 31)( 27, 35)( 28, 34)( 29, 33)( 30, 32)( 36, 50)( 37, 49)( 38, 48)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 75)( 62, 74)( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 76, 81)( 77, 85)( 78, 84)( 79, 83)( 80, 82)( 86,100)( 87, 99)( 88, 98)( 89, 97)( 90, 96)( 91, 95)( 92, 94)(101,156)(102,160)(103,159)(104,158)(105,157)(106,151)(107,155)(108,154)(109,153)(110,152)(111,175)(112,174)(113,173)(114,172)(115,171)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)(122,164)(123,163)(124,162)(125,161)(126,181)(127,185)(128,184)(129,183)(130,182)(131,176)(132,180)(133,179)(134,178)(135,177)(136,200)(137,199)(138,198)(139,197)(140,196)(141,195)(142,194)(143,193)(144,192)(145,191)(146,190)(147,189)(148,188)(149,187)(150,186); s3 := Sym(202)!(201,202); 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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 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*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*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 >;