Overview
- Group
- SmallGroup(1680,971)
- Rank
- 4
- Schläfli Type
- {105,4,2}
- Vertices, edges, …
- 105, 210, 4, 2
- Order of s0s1s2s3
- 210
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
5-fold
7-fold
35-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 25)( 6, 27)( 7, 26)( 8, 28)( 9, 21)( 10, 23)( 11, 22)( 12, 24)( 13, 17)( 14, 19)( 15, 18)( 16, 20)( 29,113)( 30,115)( 31,114)( 32,116)( 33,137)( 34,139)( 35,138)( 36,140)( 37,133)( 38,135)( 39,134)( 40,136)( 41,129)( 42,131)( 43,130)( 44,132)( 45,125)( 46,127)( 47,126)( 48,128)( 49,121)( 50,123)( 51,122)( 52,124)( 53,117)( 54,119)( 55,118)( 56,120)( 57, 85)( 58, 87)( 59, 86)( 60, 88)( 61,109)( 62,111)( 63,110)( 64,112)( 65,105)( 66,107)( 67,106)( 68,108)( 69,101)( 70,103)( 71,102)( 72,104)( 73, 97)( 74, 99)( 75, 98)( 76,100)( 77, 93)( 78, 95)( 79, 94)( 80, 96)( 81, 89)( 82, 91)( 83, 90)( 84, 92);; s1 := ( 1, 33)( 2, 36)( 3, 35)( 4, 34)( 5, 29)( 6, 32)( 7, 31)( 8, 30)( 9, 53)( 10, 56)( 11, 55)( 12, 54)( 13, 49)( 14, 52)( 15, 51)( 16, 50)( 17, 45)( 18, 48)( 19, 47)( 20, 46)( 21, 41)( 22, 44)( 23, 43)( 24, 42)( 25, 37)( 26, 40)( 27, 39)( 28, 38)( 57,117)( 58,120)( 59,119)( 60,118)( 61,113)( 62,116)( 63,115)( 64,114)( 65,137)( 66,140)( 67,139)( 68,138)( 69,133)( 70,136)( 71,135)( 72,134)( 73,129)( 74,132)( 75,131)( 76,130)( 77,125)( 78,128)( 79,127)( 80,126)( 81,121)( 82,124)( 83,123)( 84,122)( 85, 89)( 86, 92)( 87, 91)( 88, 90)( 93,109)( 94,112)( 95,111)( 96,110)( 97,105)( 98,108)( 99,107)(100,106)(102,104);; s2 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9, 12)( 10, 11)( 13, 16)( 14, 15)( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 25, 28)( 26, 27)( 29, 32)( 30, 31)( 33, 36)( 34, 35)( 37, 40)( 38, 39)( 41, 44)( 42, 43)( 45, 48)( 46, 47)( 49, 52)( 50, 51)( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)( 62, 63)( 65, 68)( 66, 67)( 69, 72)( 70, 71)( 73, 76)( 74, 75)( 77, 80)( 78, 79)( 81, 84)( 82, 83)( 85, 88)( 86, 87)( 89, 92)( 90, 91)( 93, 96)( 94, 95)( 97,100)( 98, 99)(101,104)(102,103)(105,108)(106,107)(109,112)(110,111)(113,116)(114,115)(117,120)(118,119)(121,124)(122,123)(125,128)(126,127)(129,132)(130,131)(133,136)(134,135)(137,140)(138,139);; s3 := (141,142);; 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,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s1*s0*s2*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*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*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*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*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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(142)!( 2, 3)( 5, 25)( 6, 27)( 7, 26)( 8, 28)( 9, 21)( 10, 23)( 11, 22)( 12, 24)( 13, 17)( 14, 19)( 15, 18)( 16, 20)( 29,113)( 30,115)( 31,114)( 32,116)( 33,137)( 34,139)( 35,138)( 36,140)( 37,133)( 38,135)( 39,134)( 40,136)( 41,129)( 42,131)( 43,130)( 44,132)( 45,125)( 46,127)( 47,126)( 48,128)( 49,121)( 50,123)( 51,122)( 52,124)( 53,117)( 54,119)( 55,118)( 56,120)( 57, 85)( 58, 87)( 59, 86)( 60, 88)( 61,109)( 62,111)( 63,110)( 64,112)( 65,105)( 66,107)( 67,106)( 68,108)( 69,101)( 70,103)( 71,102)( 72,104)( 73, 97)( 74, 99)( 75, 98)( 76,100)( 77, 93)( 78, 95)( 79, 94)( 80, 96)( 81, 89)( 82, 91)( 83, 90)( 84, 92); s1 := Sym(142)!( 1, 33)( 2, 36)( 3, 35)( 4, 34)( 5, 29)( 6, 32)( 7, 31)( 8, 30)( 9, 53)( 10, 56)( 11, 55)( 12, 54)( 13, 49)( 14, 52)( 15, 51)( 16, 50)( 17, 45)( 18, 48)( 19, 47)( 20, 46)( 21, 41)( 22, 44)( 23, 43)( 24, 42)( 25, 37)( 26, 40)( 27, 39)( 28, 38)( 57,117)( 58,120)( 59,119)( 60,118)( 61,113)( 62,116)( 63,115)( 64,114)( 65,137)( 66,140)( 67,139)( 68,138)( 69,133)( 70,136)( 71,135)( 72,134)( 73,129)( 74,132)( 75,131)( 76,130)( 77,125)( 78,128)( 79,127)( 80,126)( 81,121)( 82,124)( 83,123)( 84,122)( 85, 89)( 86, 92)( 87, 91)( 88, 90)( 93,109)( 94,112)( 95,111)( 96,110)( 97,105)( 98,108)( 99,107)(100,106)(102,104); s2 := Sym(142)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9, 12)( 10, 11)( 13, 16)( 14, 15)( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 25, 28)( 26, 27)( 29, 32)( 30, 31)( 33, 36)( 34, 35)( 37, 40)( 38, 39)( 41, 44)( 42, 43)( 45, 48)( 46, 47)( 49, 52)( 50, 51)( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)( 62, 63)( 65, 68)( 66, 67)( 69, 72)( 70, 71)( 73, 76)( 74, 75)( 77, 80)( 78, 79)( 81, 84)( 82, 83)( 85, 88)( 86, 87)( 89, 92)( 90, 91)( 93, 96)( 94, 95)( 97,100)( 98, 99)(101,104)(102,103)(105,108)(106,107)(109,112)(110,111)(113,116)(114,115)(117,120)(118,119)(121,124)(122,123)(125,128)(126,127)(129,132)(130,131)(133,136)(134,135)(137,140)(138,139); s3 := Sym(142)!(141,142); poly := sub<Sym(142)|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, s1*s2*s1*s2*s1*s2*s1*s2, s2*s1*s0*s2*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*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*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*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*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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;