Overview
- Group
- SmallGroup(1680,988)
- Rank
- 4
- Schläfli Type
- {2,30,14}
- Vertices, edges, …
- 2, 30, 210, 14
- 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 := (1,2);; s1 := ( 10, 31)( 11, 32)( 12, 33)( 13, 34)( 14, 35)( 15, 36)( 16, 37)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 22, 29)( 23, 30)( 38, 73)( 39, 74)( 40, 75)( 41, 76)( 42, 77)( 43, 78)( 44, 79)( 45,101)( 46,102)( 47,103)( 48,104)( 49,105)( 50,106)( 51,107)( 52, 94)( 53, 95)( 54, 96)( 55, 97)( 56, 98)( 57, 99)( 58,100)( 59, 87)( 60, 88)( 61, 89)( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 80)( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 71, 85)( 72, 86)(115,136)(116,137)(117,138)(118,139)(119,140)(120,141)(121,142)(122,129)(123,130)(124,131)(125,132)(126,133)(127,134)(128,135)(143,178)(144,179)(145,180)(146,181)(147,182)(148,183)(149,184)(150,206)(151,207)(152,208)(153,209)(154,210)(155,211)(156,212)(157,199)(158,200)(159,201)(160,202)(161,203)(162,204)(163,205)(164,192)(165,193)(166,194)(167,195)(168,196)(169,197)(170,198)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191);; s2 := ( 3, 45)( 4, 51)( 5, 50)( 6, 49)( 7, 48)( 8, 47)( 9, 46)( 10, 38)( 11, 44)( 12, 43)( 13, 42)( 14, 41)( 15, 40)( 16, 39)( 17, 66)( 18, 72)( 19, 71)( 20, 70)( 21, 69)( 22, 68)( 23, 67)( 24, 59)( 25, 65)( 26, 64)( 27, 63)( 28, 62)( 29, 61)( 30, 60)( 31, 52)( 32, 58)( 33, 57)( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 73, 80)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)( 79, 81)( 87,101)( 88,107)( 89,106)( 90,105)( 91,104)( 92,103)( 93,102)( 95,100)( 96, 99)( 97, 98)(108,150)(109,156)(110,155)(111,154)(112,153)(113,152)(114,151)(115,143)(116,149)(117,148)(118,147)(119,146)(120,145)(121,144)(122,171)(123,177)(124,176)(125,175)(126,174)(127,173)(128,172)(129,164)(130,170)(131,169)(132,168)(133,167)(134,166)(135,165)(136,157)(137,163)(138,162)(139,161)(140,160)(141,159)(142,158)(178,185)(179,191)(180,190)(181,189)(182,188)(183,187)(184,186)(192,206)(193,212)(194,211)(195,210)(196,209)(197,208)(198,207)(200,205)(201,204)(202,203);; s3 := ( 3,109)( 4,108)( 5,114)( 6,113)( 7,112)( 8,111)( 9,110)( 10,116)( 11,115)( 12,121)( 13,120)( 14,119)( 15,118)( 16,117)( 17,123)( 18,122)( 19,128)( 20,127)( 21,126)( 22,125)( 23,124)( 24,130)( 25,129)( 26,135)( 27,134)( 28,133)( 29,132)( 30,131)( 31,137)( 32,136)( 33,142)( 34,141)( 35,140)( 36,139)( 37,138)( 38,144)( 39,143)( 40,149)( 41,148)( 42,147)( 43,146)( 44,145)( 45,151)( 46,150)( 47,156)( 48,155)( 49,154)( 50,153)( 51,152)( 52,158)( 53,157)( 54,163)( 55,162)( 56,161)( 57,160)( 58,159)( 59,165)( 60,164)( 61,170)( 62,169)( 63,168)( 64,167)( 65,166)( 66,172)( 67,171)( 68,177)( 69,176)( 70,175)( 71,174)( 72,173)( 73,179)( 74,178)( 75,184)( 76,183)( 77,182)( 78,181)( 79,180)( 80,186)( 81,185)( 82,191)( 83,190)( 84,189)( 85,188)( 86,187)( 87,193)( 88,192)( 89,198)( 90,197)( 91,196)( 92,195)( 93,194)( 94,200)( 95,199)( 96,205)( 97,204)( 98,203)( 99,202)(100,201)(101,207)(102,206)(103,212)(104,211)(105,210)(106,209)(107,208);; 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(212)!(1,2); s1 := Sym(212)!( 10, 31)( 11, 32)( 12, 33)( 13, 34)( 14, 35)( 15, 36)( 16, 37)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 22, 29)( 23, 30)( 38, 73)( 39, 74)( 40, 75)( 41, 76)( 42, 77)( 43, 78)( 44, 79)( 45,101)( 46,102)( 47,103)( 48,104)( 49,105)( 50,106)( 51,107)( 52, 94)( 53, 95)( 54, 96)( 55, 97)( 56, 98)( 57, 99)( 58,100)( 59, 87)( 60, 88)( 61, 89)( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 80)( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 71, 85)( 72, 86)(115,136)(116,137)(117,138)(118,139)(119,140)(120,141)(121,142)(122,129)(123,130)(124,131)(125,132)(126,133)(127,134)(128,135)(143,178)(144,179)(145,180)(146,181)(147,182)(148,183)(149,184)(150,206)(151,207)(152,208)(153,209)(154,210)(155,211)(156,212)(157,199)(158,200)(159,201)(160,202)(161,203)(162,204)(163,205)(164,192)(165,193)(166,194)(167,195)(168,196)(169,197)(170,198)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191); s2 := Sym(212)!( 3, 45)( 4, 51)( 5, 50)( 6, 49)( 7, 48)( 8, 47)( 9, 46)( 10, 38)( 11, 44)( 12, 43)( 13, 42)( 14, 41)( 15, 40)( 16, 39)( 17, 66)( 18, 72)( 19, 71)( 20, 70)( 21, 69)( 22, 68)( 23, 67)( 24, 59)( 25, 65)( 26, 64)( 27, 63)( 28, 62)( 29, 61)( 30, 60)( 31, 52)( 32, 58)( 33, 57)( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 73, 80)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)( 79, 81)( 87,101)( 88,107)( 89,106)( 90,105)( 91,104)( 92,103)( 93,102)( 95,100)( 96, 99)( 97, 98)(108,150)(109,156)(110,155)(111,154)(112,153)(113,152)(114,151)(115,143)(116,149)(117,148)(118,147)(119,146)(120,145)(121,144)(122,171)(123,177)(124,176)(125,175)(126,174)(127,173)(128,172)(129,164)(130,170)(131,169)(132,168)(133,167)(134,166)(135,165)(136,157)(137,163)(138,162)(139,161)(140,160)(141,159)(142,158)(178,185)(179,191)(180,190)(181,189)(182,188)(183,187)(184,186)(192,206)(193,212)(194,211)(195,210)(196,209)(197,208)(198,207)(200,205)(201,204)(202,203); s3 := Sym(212)!( 3,109)( 4,108)( 5,114)( 6,113)( 7,112)( 8,111)( 9,110)( 10,116)( 11,115)( 12,121)( 13,120)( 14,119)( 15,118)( 16,117)( 17,123)( 18,122)( 19,128)( 20,127)( 21,126)( 22,125)( 23,124)( 24,130)( 25,129)( 26,135)( 27,134)( 28,133)( 29,132)( 30,131)( 31,137)( 32,136)( 33,142)( 34,141)( 35,140)( 36,139)( 37,138)( 38,144)( 39,143)( 40,149)( 41,148)( 42,147)( 43,146)( 44,145)( 45,151)( 46,150)( 47,156)( 48,155)( 49,154)( 50,153)( 51,152)( 52,158)( 53,157)( 54,163)( 55,162)( 56,161)( 57,160)( 58,159)( 59,165)( 60,164)( 61,170)( 62,169)( 63,168)( 64,167)( 65,166)( 66,172)( 67,171)( 68,177)( 69,176)( 70,175)( 71,174)( 72,173)( 73,179)( 74,178)( 75,184)( 76,183)( 77,182)( 78,181)( 79,180)( 80,186)( 81,185)( 82,191)( 83,190)( 84,189)( 85,188)( 86,187)( 87,193)( 88,192)( 89,198)( 90,197)( 91,196)( 92,195)( 93,194)( 94,200)( 95,199)( 96,205)( 97,204)( 98,203)( 99,202)(100,201)(101,207)(102,206)(103,212)(104,211)(105,210)(106,209)(107,208); 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*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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 >;