Overview
- Group
- SmallGroup(1568,877)
- Rank
- 4
- Schläfli Type
- {2,28,14}
- Vertices, edges, …
- 2, 28, 196, 14
- Order of s0s1s2s3
- 28
- 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
7-fold
14-fold
28-fold
49-fold
98-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 9)( 5, 8)( 6, 7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)( 19, 22)( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)( 39, 44)( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)( 55, 56)( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)( 75, 78)( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)( 95,100)( 96, 99)( 97, 98)(101,150)(102,156)(103,155)(104,154)(105,153)(106,152)(107,151)(108,157)(109,163)(110,162)(111,161)(112,160)(113,159)(114,158)(115,164)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)(122,171)(123,177)(124,176)(125,175)(126,174)(127,173)(128,172)(129,178)(130,184)(131,183)(132,182)(133,181)(134,180)(135,179)(136,185)(137,191)(138,190)(139,189)(140,188)(141,187)(142,186)(143,192)(144,198)(145,197)(146,196)(147,195)(148,194)(149,193);; s2 := ( 3,102)( 4,101)( 5,107)( 6,106)( 7,105)( 8,104)( 9,103)( 10,144)( 11,143)( 12,149)( 13,148)( 14,147)( 15,146)( 16,145)( 17,137)( 18,136)( 19,142)( 20,141)( 21,140)( 22,139)( 23,138)( 24,130)( 25,129)( 26,135)( 27,134)( 28,133)( 29,132)( 30,131)( 31,123)( 32,122)( 33,128)( 34,127)( 35,126)( 36,125)( 37,124)( 38,116)( 39,115)( 40,121)( 41,120)( 42,119)( 43,118)( 44,117)( 45,109)( 46,108)( 47,114)( 48,113)( 49,112)( 50,111)( 51,110)( 52,151)( 53,150)( 54,156)( 55,155)( 56,154)( 57,153)( 58,152)( 59,193)( 60,192)( 61,198)( 62,197)( 63,196)( 64,195)( 65,194)( 66,186)( 67,185)( 68,191)( 69,190)( 70,189)( 71,188)( 72,187)( 73,179)( 74,178)( 75,184)( 76,183)( 77,182)( 78,181)( 79,180)( 80,172)( 81,171)( 82,177)( 83,176)( 84,175)( 85,174)( 86,173)( 87,165)( 88,164)( 89,170)( 90,169)( 91,168)( 92,167)( 93,166)( 94,158)( 95,157)( 96,163)( 97,162)( 98,161)( 99,160)(100,159);; s3 := ( 3, 10)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)( 9, 11)( 17, 45)( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)( 23, 46)( 24, 38)( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 32, 37)( 33, 36)( 34, 35)( 52, 59)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)( 58, 60)( 66, 94)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)( 72, 95)( 73, 87)( 74, 93)( 75, 92)( 76, 91)( 77, 90)( 78, 89)( 79, 88)( 81, 86)( 82, 85)( 83, 84)(101,108)(102,114)(103,113)(104,112)(105,111)(106,110)(107,109)(115,143)(116,149)(117,148)(118,147)(119,146)(120,145)(121,144)(122,136)(123,142)(124,141)(125,140)(126,139)(127,138)(128,137)(130,135)(131,134)(132,133)(150,157)(151,163)(152,162)(153,161)(154,160)(155,159)(156,158)(164,192)(165,198)(166,197)(167,196)(168,195)(169,194)(170,193)(171,185)(172,191)(173,190)(174,189)(175,188)(176,187)(177,186)(179,184)(180,183)(181,182);; 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*s1*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(198)!(1,2); s1 := Sym(198)!( 4, 9)( 5, 8)( 6, 7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)( 19, 22)( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)( 39, 44)( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)( 55, 56)( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)( 75, 78)( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)( 95,100)( 96, 99)( 97, 98)(101,150)(102,156)(103,155)(104,154)(105,153)(106,152)(107,151)(108,157)(109,163)(110,162)(111,161)(112,160)(113,159)(114,158)(115,164)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)(122,171)(123,177)(124,176)(125,175)(126,174)(127,173)(128,172)(129,178)(130,184)(131,183)(132,182)(133,181)(134,180)(135,179)(136,185)(137,191)(138,190)(139,189)(140,188)(141,187)(142,186)(143,192)(144,198)(145,197)(146,196)(147,195)(148,194)(149,193); s2 := Sym(198)!( 3,102)( 4,101)( 5,107)( 6,106)( 7,105)( 8,104)( 9,103)( 10,144)( 11,143)( 12,149)( 13,148)( 14,147)( 15,146)( 16,145)( 17,137)( 18,136)( 19,142)( 20,141)( 21,140)( 22,139)( 23,138)( 24,130)( 25,129)( 26,135)( 27,134)( 28,133)( 29,132)( 30,131)( 31,123)( 32,122)( 33,128)( 34,127)( 35,126)( 36,125)( 37,124)( 38,116)( 39,115)( 40,121)( 41,120)( 42,119)( 43,118)( 44,117)( 45,109)( 46,108)( 47,114)( 48,113)( 49,112)( 50,111)( 51,110)( 52,151)( 53,150)( 54,156)( 55,155)( 56,154)( 57,153)( 58,152)( 59,193)( 60,192)( 61,198)( 62,197)( 63,196)( 64,195)( 65,194)( 66,186)( 67,185)( 68,191)( 69,190)( 70,189)( 71,188)( 72,187)( 73,179)( 74,178)( 75,184)( 76,183)( 77,182)( 78,181)( 79,180)( 80,172)( 81,171)( 82,177)( 83,176)( 84,175)( 85,174)( 86,173)( 87,165)( 88,164)( 89,170)( 90,169)( 91,168)( 92,167)( 93,166)( 94,158)( 95,157)( 96,163)( 97,162)( 98,161)( 99,160)(100,159); s3 := Sym(198)!( 3, 10)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)( 9, 11)( 17, 45)( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)( 23, 46)( 24, 38)( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 32, 37)( 33, 36)( 34, 35)( 52, 59)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)( 58, 60)( 66, 94)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)( 72, 95)( 73, 87)( 74, 93)( 75, 92)( 76, 91)( 77, 90)( 78, 89)( 79, 88)( 81, 86)( 82, 85)( 83, 84)(101,108)(102,114)(103,113)(104,112)(105,111)(106,110)(107,109)(115,143)(116,149)(117,148)(118,147)(119,146)(120,145)(121,144)(122,136)(123,142)(124,141)(125,140)(126,139)(127,138)(128,137)(130,135)(131,134)(132,133)(150,157)(151,163)(152,162)(153,161)(154,160)(155,159)(156,158)(164,192)(165,198)(166,197)(167,196)(168,195)(169,194)(170,193)(171,185)(172,191)(173,190)(174,189)(175,188)(176,187)(177,186)(179,184)(180,183)(181,182); poly := sub<Sym(198)|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*s1*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;