Overview
- Group
- SmallGroup(1696,182)
- Rank
- 4
- Schläfli Type
- {2,106,4}
- Vertices, edges, …
- 2, 106, 212, 4
- Order of s0s1s2s3
- 212
- 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
53-fold
106-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 55)( 5, 54)( 6, 53)( 7, 52)( 8, 51)( 9, 50)( 10, 49)( 11, 48)( 12, 47)( 13, 46)( 14, 45)( 15, 44)( 16, 43)( 17, 42)( 18, 41)( 19, 40)( 20, 39)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)( 27, 32)( 28, 31)( 29, 30)( 57,108)( 58,107)( 59,106)( 60,105)( 61,104)( 62,103)( 63,102)( 64,101)( 65,100)( 66, 99)( 67, 98)( 68, 97)( 69, 96)( 70, 95)( 71, 94)( 72, 93)( 73, 92)( 74, 91)( 75, 90)( 76, 89)( 77, 88)( 78, 87)( 79, 86)( 80, 85)( 81, 84)( 82, 83)(110,161)(111,160)(112,159)(113,158)(114,157)(115,156)(116,155)(117,154)(118,153)(119,152)(120,151)(121,150)(122,149)(123,148)(124,147)(125,146)(126,145)(127,144)(128,143)(129,142)(130,141)(131,140)(132,139)(133,138)(134,137)(135,136)(163,214)(164,213)(165,212)(166,211)(167,210)(168,209)(169,208)(170,207)(171,206)(172,205)(173,204)(174,203)(175,202)(176,201)(177,200)(178,199)(179,198)(180,197)(181,196)(182,195)(183,194)(184,193)(185,192)(186,191)(187,190)(188,189);; s2 := ( 3, 4)( 5, 55)( 6, 54)( 7, 53)( 8, 52)( 9, 51)( 10, 50)( 11, 49)( 12, 48)( 13, 47)( 14, 46)( 15, 45)( 16, 44)( 17, 43)( 18, 42)( 19, 41)( 20, 40)( 21, 39)( 22, 38)( 23, 37)( 24, 36)( 25, 35)( 26, 34)( 27, 33)( 28, 32)( 29, 31)( 56, 57)( 58,108)( 59,107)( 60,106)( 61,105)( 62,104)( 63,103)( 64,102)( 65,101)( 66,100)( 67, 99)( 68, 98)( 69, 97)( 70, 96)( 71, 95)( 72, 94)( 73, 93)( 74, 92)( 75, 91)( 76, 90)( 77, 89)( 78, 88)( 79, 87)( 80, 86)( 81, 85)( 82, 84)(109,163)(110,162)(111,214)(112,213)(113,212)(114,211)(115,210)(116,209)(117,208)(118,207)(119,206)(120,205)(121,204)(122,203)(123,202)(124,201)(125,200)(126,199)(127,198)(128,197)(129,196)(130,195)(131,194)(132,193)(133,192)(134,191)(135,190)(136,189)(137,188)(138,187)(139,186)(140,185)(141,184)(142,183)(143,182)(144,181)(145,180)(146,179)(147,178)(148,177)(149,176)(150,175)(151,174)(152,173)(153,172)(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164);; s3 := ( 3,109)( 4,110)( 5,111)( 6,112)( 7,113)( 8,114)( 9,115)( 10,116)( 11,117)( 12,118)( 13,119)( 14,120)( 15,121)( 16,122)( 17,123)( 18,124)( 19,125)( 20,126)( 21,127)( 22,128)( 23,129)( 24,130)( 25,131)( 26,132)( 27,133)( 28,134)( 29,135)( 30,136)( 31,137)( 32,138)( 33,139)( 34,140)( 35,141)( 36,142)( 37,143)( 38,144)( 39,145)( 40,146)( 41,147)( 42,148)( 43,149)( 44,150)( 45,151)( 46,152)( 47,153)( 48,154)( 49,155)( 50,156)( 51,157)( 52,158)( 53,159)( 54,160)( 55,161)( 56,162)( 57,163)( 58,164)( 59,165)( 60,166)( 61,167)( 62,168)( 63,169)( 64,170)( 65,171)( 66,172)( 67,173)( 68,174)( 69,175)( 70,176)( 71,177)( 72,178)( 73,179)( 74,180)( 75,181)( 76,182)( 77,183)( 78,184)( 79,185)( 80,186)( 81,187)( 82,188)( 83,189)( 84,190)( 85,191)( 86,192)( 87,193)( 88,194)( 89,195)( 90,196)( 91,197)( 92,198)( 93,199)( 94,200)( 95,201)( 96,202)( 97,203)( 98,204)( 99,205)(100,206)(101,207)(102,208)(103,209)(104,210)(105,211)(106,212)(107,213)(108,214);; 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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(214)!(1,2); s1 := Sym(214)!( 4, 55)( 5, 54)( 6, 53)( 7, 52)( 8, 51)( 9, 50)( 10, 49)( 11, 48)( 12, 47)( 13, 46)( 14, 45)( 15, 44)( 16, 43)( 17, 42)( 18, 41)( 19, 40)( 20, 39)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)( 27, 32)( 28, 31)( 29, 30)( 57,108)( 58,107)( 59,106)( 60,105)( 61,104)( 62,103)( 63,102)( 64,101)( 65,100)( 66, 99)( 67, 98)( 68, 97)( 69, 96)( 70, 95)( 71, 94)( 72, 93)( 73, 92)( 74, 91)( 75, 90)( 76, 89)( 77, 88)( 78, 87)( 79, 86)( 80, 85)( 81, 84)( 82, 83)(110,161)(111,160)(112,159)(113,158)(114,157)(115,156)(116,155)(117,154)(118,153)(119,152)(120,151)(121,150)(122,149)(123,148)(124,147)(125,146)(126,145)(127,144)(128,143)(129,142)(130,141)(131,140)(132,139)(133,138)(134,137)(135,136)(163,214)(164,213)(165,212)(166,211)(167,210)(168,209)(169,208)(170,207)(171,206)(172,205)(173,204)(174,203)(175,202)(176,201)(177,200)(178,199)(179,198)(180,197)(181,196)(182,195)(183,194)(184,193)(185,192)(186,191)(187,190)(188,189); s2 := Sym(214)!( 3, 4)( 5, 55)( 6, 54)( 7, 53)( 8, 52)( 9, 51)( 10, 50)( 11, 49)( 12, 48)( 13, 47)( 14, 46)( 15, 45)( 16, 44)( 17, 43)( 18, 42)( 19, 41)( 20, 40)( 21, 39)( 22, 38)( 23, 37)( 24, 36)( 25, 35)( 26, 34)( 27, 33)( 28, 32)( 29, 31)( 56, 57)( 58,108)( 59,107)( 60,106)( 61,105)( 62,104)( 63,103)( 64,102)( 65,101)( 66,100)( 67, 99)( 68, 98)( 69, 97)( 70, 96)( 71, 95)( 72, 94)( 73, 93)( 74, 92)( 75, 91)( 76, 90)( 77, 89)( 78, 88)( 79, 87)( 80, 86)( 81, 85)( 82, 84)(109,163)(110,162)(111,214)(112,213)(113,212)(114,211)(115,210)(116,209)(117,208)(118,207)(119,206)(120,205)(121,204)(122,203)(123,202)(124,201)(125,200)(126,199)(127,198)(128,197)(129,196)(130,195)(131,194)(132,193)(133,192)(134,191)(135,190)(136,189)(137,188)(138,187)(139,186)(140,185)(141,184)(142,183)(143,182)(144,181)(145,180)(146,179)(147,178)(148,177)(149,176)(150,175)(151,174)(152,173)(153,172)(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164); s3 := Sym(214)!( 3,109)( 4,110)( 5,111)( 6,112)( 7,113)( 8,114)( 9,115)( 10,116)( 11,117)( 12,118)( 13,119)( 14,120)( 15,121)( 16,122)( 17,123)( 18,124)( 19,125)( 20,126)( 21,127)( 22,128)( 23,129)( 24,130)( 25,131)( 26,132)( 27,133)( 28,134)( 29,135)( 30,136)( 31,137)( 32,138)( 33,139)( 34,140)( 35,141)( 36,142)( 37,143)( 38,144)( 39,145)( 40,146)( 41,147)( 42,148)( 43,149)( 44,150)( 45,151)( 46,152)( 47,153)( 48,154)( 49,155)( 50,156)( 51,157)( 52,158)( 53,159)( 54,160)( 55,161)( 56,162)( 57,163)( 58,164)( 59,165)( 60,166)( 61,167)( 62,168)( 63,169)( 64,170)( 65,171)( 66,172)( 67,173)( 68,174)( 69,175)( 70,176)( 71,177)( 72,178)( 73,179)( 74,180)( 75,181)( 76,182)( 77,183)( 78,184)( 79,185)( 80,186)( 81,187)( 82,188)( 83,189)( 84,190)( 85,191)( 86,192)( 87,193)( 88,194)( 89,195)( 90,196)( 91,197)( 92,198)( 93,199)( 94,200)( 95,201)( 96,202)( 97,203)( 98,204)( 99,205)(100,206)(101,207)(102,208)(103,209)(104,210)(105,211)(106,212)(107,213)(108,214); poly := sub<Sym(214)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;