Overview
- Group
- SmallGroup(1120,998)
- Rank
- 4
- Schläfli Type
- {4,14,10}
- Vertices, edges, …
- 4, 28, 70, 10
- Order of s0s1s2s3
- 140
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{4,14|2},{14,10|2}}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
5-fold
7-fold
10-fold
14-fold
20-fold
28-fold
35-fold
70-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)( 76,111)( 77,112)( 78,113)( 79,114)( 80,115)( 81,116)( 82,117)( 83,118)( 84,119)( 85,120)( 86,121)( 87,122)( 88,123)( 89,124)( 90,125)( 91,126)( 92,127)( 93,128)( 94,129)( 95,130)( 96,131)( 97,132)( 98,133)( 99,134)(100,135)(101,136)(102,137)(103,138)(104,139)(105,140);; s1 := ( 1, 71)( 2, 77)( 3, 76)( 4, 75)( 5, 74)( 6, 73)( 7, 72)( 8, 78)( 9, 84)( 10, 83)( 11, 82)( 12, 81)( 13, 80)( 14, 79)( 15, 85)( 16, 91)( 17, 90)( 18, 89)( 19, 88)( 20, 87)( 21, 86)( 22, 92)( 23, 98)( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 99)( 30,105)( 31,104)( 32,103)( 33,102)( 34,101)( 35,100)( 36,106)( 37,112)( 38,111)( 39,110)( 40,109)( 41,108)( 42,107)( 43,113)( 44,119)( 45,118)( 46,117)( 47,116)( 48,115)( 49,114)( 50,120)( 51,126)( 52,125)( 53,124)( 54,123)( 55,122)( 56,121)( 57,127)( 58,133)( 59,132)( 60,131)( 61,130)( 62,129)( 63,128)( 64,134)( 65,140)( 66,139)( 67,138)( 68,137)( 69,136)( 70,135);; s2 := ( 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, 37)( 38, 42)( 39, 41)( 43, 65)( 44, 64)( 45, 70)( 46, 69)( 47, 68)( 48, 67)( 49, 66)( 50, 58)( 51, 57)( 52, 63)( 53, 62)( 54, 61)( 55, 60)( 56, 59)( 71, 72)( 73, 77)( 74, 76)( 78,100)( 79, 99)( 80,105)( 81,104)( 82,103)( 83,102)( 84,101)( 85, 93)( 86, 92)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)(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);; s3 := ( 1, 8)( 2, 9)( 3, 10)( 4, 11)( 5, 12)( 6, 13)( 7, 14)( 15, 29)( 16, 30)( 17, 31)( 18, 32)( 19, 33)( 20, 34)( 21, 35)( 36, 43)( 37, 44)( 38, 45)( 39, 46)( 40, 47)( 41, 48)( 42, 49)( 50, 64)( 51, 65)( 52, 66)( 53, 67)( 54, 68)( 55, 69)( 56, 70)( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)( 85, 99)( 86,100)( 87,101)( 88,102)( 89,103)( 90,104)( 91,105)(106,113)(107,114)(108,115)(109,116)(110,117)(111,118)(112,119)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140);; 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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, 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,
s1*s2*s1*s2*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(140)!( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)( 76,111)( 77,112)( 78,113)( 79,114)( 80,115)( 81,116)( 82,117)( 83,118)( 84,119)( 85,120)( 86,121)( 87,122)( 88,123)( 89,124)( 90,125)( 91,126)( 92,127)( 93,128)( 94,129)( 95,130)( 96,131)( 97,132)( 98,133)( 99,134)(100,135)(101,136)(102,137)(103,138)(104,139)(105,140); s1 := Sym(140)!( 1, 71)( 2, 77)( 3, 76)( 4, 75)( 5, 74)( 6, 73)( 7, 72)( 8, 78)( 9, 84)( 10, 83)( 11, 82)( 12, 81)( 13, 80)( 14, 79)( 15, 85)( 16, 91)( 17, 90)( 18, 89)( 19, 88)( 20, 87)( 21, 86)( 22, 92)( 23, 98)( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 99)( 30,105)( 31,104)( 32,103)( 33,102)( 34,101)( 35,100)( 36,106)( 37,112)( 38,111)( 39,110)( 40,109)( 41,108)( 42,107)( 43,113)( 44,119)( 45,118)( 46,117)( 47,116)( 48,115)( 49,114)( 50,120)( 51,126)( 52,125)( 53,124)( 54,123)( 55,122)( 56,121)( 57,127)( 58,133)( 59,132)( 60,131)( 61,130)( 62,129)( 63,128)( 64,134)( 65,140)( 66,139)( 67,138)( 68,137)( 69,136)( 70,135); s2 := Sym(140)!( 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, 37)( 38, 42)( 39, 41)( 43, 65)( 44, 64)( 45, 70)( 46, 69)( 47, 68)( 48, 67)( 49, 66)( 50, 58)( 51, 57)( 52, 63)( 53, 62)( 54, 61)( 55, 60)( 56, 59)( 71, 72)( 73, 77)( 74, 76)( 78,100)( 79, 99)( 80,105)( 81,104)( 82,103)( 83,102)( 84,101)( 85, 93)( 86, 92)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)(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); s3 := Sym(140)!( 1, 8)( 2, 9)( 3, 10)( 4, 11)( 5, 12)( 6, 13)( 7, 14)( 15, 29)( 16, 30)( 17, 31)( 18, 32)( 19, 33)( 20, 34)( 21, 35)( 36, 43)( 37, 44)( 38, 45)( 39, 46)( 40, 47)( 41, 48)( 42, 49)( 50, 64)( 51, 65)( 52, 66)( 53, 67)( 54, 68)( 55, 69)( 56, 70)( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)( 85, 99)( 86,100)( 87,101)( 88,102)( 89,103)( 90,104)( 91,105)(106,113)(107,114)(108,115)(109,116)(110,117)(111,118)(112,119)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140); poly := sub<Sym(140)|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, s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.