Overview
- Group
- SmallGroup(1680,988)
- Rank
- 4
- Schläfli Type
- {14,30,2}
- Vertices, edges, …
- 14, 210, 30, 2
- Order of s0s1s2s3
- 210
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
7-fold
14-fold
15-fold
21-fold
30-fold
35-fold
42-fold
70-fold
105-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)( 93, 98)( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)(109,110)(114,119)(115,118)(116,117)(121,126)(122,125)(123,124)(128,133)(129,132)(130,131)(135,140)(136,139)(137,138)(142,147)(143,146)(144,145)(149,154)(150,153)(151,152)(156,161)(157,160)(158,159)(163,168)(164,167)(165,166)(170,175)(171,174)(172,173)(177,182)(178,181)(179,180)(184,189)(185,188)(186,187)(191,196)(192,195)(193,194)(198,203)(199,202)(200,201)(205,210)(206,209)(207,208);; s1 := ( 1, 2)( 3, 7)( 4, 6)( 8, 30)( 9, 29)( 10, 35)( 11, 34)( 12, 33)( 13, 32)( 14, 31)( 15, 23)( 16, 22)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 36, 72)( 37, 71)( 38, 77)( 39, 76)( 40, 75)( 41, 74)( 42, 73)( 43,100)( 44, 99)( 45,105)( 46,104)( 47,103)( 48,102)( 49,101)( 50, 93)( 51, 92)( 52, 98)( 53, 97)( 54, 96)( 55, 95)( 56, 94)( 57, 86)( 58, 85)( 59, 91)( 60, 90)( 61, 89)( 62, 88)( 63, 87)( 64, 79)( 65, 78)( 66, 84)( 67, 83)( 68, 82)( 69, 81)( 70, 80)(106,107)(108,112)(109,111)(113,135)(114,134)(115,140)(116,139)(117,138)(118,137)(119,136)(120,128)(121,127)(122,133)(123,132)(124,131)(125,130)(126,129)(141,177)(142,176)(143,182)(144,181)(145,180)(146,179)(147,178)(148,205)(149,204)(150,210)(151,209)(152,208)(153,207)(154,206)(155,198)(156,197)(157,203)(158,202)(159,201)(160,200)(161,199)(162,191)(163,190)(164,196)(165,195)(166,194)(167,193)(168,192)(169,184)(170,183)(171,189)(172,188)(173,187)(174,186)(175,185);; s2 := ( 1,148)( 2,149)( 3,150)( 4,151)( 5,152)( 6,153)( 7,154)( 8,141)( 9,142)( 10,143)( 11,144)( 12,145)( 13,146)( 14,147)( 15,169)( 16,170)( 17,171)( 18,172)( 19,173)( 20,174)( 21,175)( 22,162)( 23,163)( 24,164)( 25,165)( 26,166)( 27,167)( 28,168)( 29,155)( 30,156)( 31,157)( 32,158)( 33,159)( 34,160)( 35,161)( 36,113)( 37,114)( 38,115)( 39,116)( 40,117)( 41,118)( 42,119)( 43,106)( 44,107)( 45,108)( 46,109)( 47,110)( 48,111)( 49,112)( 50,134)( 51,135)( 52,136)( 53,137)( 54,138)( 55,139)( 56,140)( 57,127)( 58,128)( 59,129)( 60,130)( 61,131)( 62,132)( 63,133)( 64,120)( 65,121)( 66,122)( 67,123)( 68,124)( 69,125)( 70,126)( 71,183)( 72,184)( 73,185)( 74,186)( 75,187)( 76,188)( 77,189)( 78,176)( 79,177)( 80,178)( 81,179)( 82,180)( 83,181)( 84,182)( 85,204)( 86,205)( 87,206)( 88,207)( 89,208)( 90,209)( 91,210)( 92,197)( 93,198)( 94,199)( 95,200)( 96,201)( 97,202)( 98,203)( 99,190)(100,191)(101,192)(102,193)(103,194)(104,195)(105,196);; s3 := (211,212);; 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*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(212)!( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)( 93, 98)( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)(109,110)(114,119)(115,118)(116,117)(121,126)(122,125)(123,124)(128,133)(129,132)(130,131)(135,140)(136,139)(137,138)(142,147)(143,146)(144,145)(149,154)(150,153)(151,152)(156,161)(157,160)(158,159)(163,168)(164,167)(165,166)(170,175)(171,174)(172,173)(177,182)(178,181)(179,180)(184,189)(185,188)(186,187)(191,196)(192,195)(193,194)(198,203)(199,202)(200,201)(205,210)(206,209)(207,208); s1 := Sym(212)!( 1, 2)( 3, 7)( 4, 6)( 8, 30)( 9, 29)( 10, 35)( 11, 34)( 12, 33)( 13, 32)( 14, 31)( 15, 23)( 16, 22)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 36, 72)( 37, 71)( 38, 77)( 39, 76)( 40, 75)( 41, 74)( 42, 73)( 43,100)( 44, 99)( 45,105)( 46,104)( 47,103)( 48,102)( 49,101)( 50, 93)( 51, 92)( 52, 98)( 53, 97)( 54, 96)( 55, 95)( 56, 94)( 57, 86)( 58, 85)( 59, 91)( 60, 90)( 61, 89)( 62, 88)( 63, 87)( 64, 79)( 65, 78)( 66, 84)( 67, 83)( 68, 82)( 69, 81)( 70, 80)(106,107)(108,112)(109,111)(113,135)(114,134)(115,140)(116,139)(117,138)(118,137)(119,136)(120,128)(121,127)(122,133)(123,132)(124,131)(125,130)(126,129)(141,177)(142,176)(143,182)(144,181)(145,180)(146,179)(147,178)(148,205)(149,204)(150,210)(151,209)(152,208)(153,207)(154,206)(155,198)(156,197)(157,203)(158,202)(159,201)(160,200)(161,199)(162,191)(163,190)(164,196)(165,195)(166,194)(167,193)(168,192)(169,184)(170,183)(171,189)(172,188)(173,187)(174,186)(175,185); s2 := Sym(212)!( 1,148)( 2,149)( 3,150)( 4,151)( 5,152)( 6,153)( 7,154)( 8,141)( 9,142)( 10,143)( 11,144)( 12,145)( 13,146)( 14,147)( 15,169)( 16,170)( 17,171)( 18,172)( 19,173)( 20,174)( 21,175)( 22,162)( 23,163)( 24,164)( 25,165)( 26,166)( 27,167)( 28,168)( 29,155)( 30,156)( 31,157)( 32,158)( 33,159)( 34,160)( 35,161)( 36,113)( 37,114)( 38,115)( 39,116)( 40,117)( 41,118)( 42,119)( 43,106)( 44,107)( 45,108)( 46,109)( 47,110)( 48,111)( 49,112)( 50,134)( 51,135)( 52,136)( 53,137)( 54,138)( 55,139)( 56,140)( 57,127)( 58,128)( 59,129)( 60,130)( 61,131)( 62,132)( 63,133)( 64,120)( 65,121)( 66,122)( 67,123)( 68,124)( 69,125)( 70,126)( 71,183)( 72,184)( 73,185)( 74,186)( 75,187)( 76,188)( 77,189)( 78,176)( 79,177)( 80,178)( 81,179)( 82,180)( 83,181)( 84,182)( 85,204)( 86,205)( 87,206)( 88,207)( 89,208)( 90,209)( 91,210)( 92,197)( 93,198)( 94,199)( 95,200)( 96,201)( 97,202)( 98,203)( 99,190)(100,191)(101,192)(102,193)(103,194)(104,195)(105,196); s3 := Sym(212)!(211,212); poly := sub<Sym(212)|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*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 >;