Overview
- Group
- SmallGroup(1152,133451)
- Rank
- 4
- Schläfli Type
- {2,48,6}
- Vertices, edges, …
- 2, 48, 144, 6
- Order of s0s1s2s3
- 48
- 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
3-fold
4-fold
6-fold
8-fold
9-fold
12-fold
16-fold
18-fold
24-fold
36-fold
48-fold
72-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)( 21, 30)( 22, 32)( 23, 31)( 24, 36)( 25, 38)( 26, 37)( 27, 33)( 28, 35)( 29, 34)( 39, 57)( 40, 59)( 41, 58)( 42, 63)( 43, 65)( 44, 64)( 45, 60)( 46, 62)( 47, 61)( 48, 66)( 49, 68)( 50, 67)( 51, 72)( 52, 74)( 53, 73)( 54, 69)( 55, 71)( 56, 70)( 75,111)( 76,113)( 77,112)( 78,117)( 79,119)( 80,118)( 81,114)( 82,116)( 83,115)( 84,120)( 85,122)( 86,121)( 87,126)( 88,128)( 89,127)( 90,123)( 91,125)( 92,124)( 93,138)( 94,140)( 95,139)( 96,144)( 97,146)( 98,145)( 99,141)(100,143)(101,142)(102,129)(103,131)(104,130)(105,135)(106,137)(107,136)(108,132)(109,134)(110,133);; s2 := ( 3, 79)( 4, 78)( 5, 80)( 6, 76)( 7, 75)( 8, 77)( 9, 82)( 10, 81)( 11, 83)( 12, 88)( 13, 87)( 14, 89)( 15, 85)( 16, 84)( 17, 86)( 18, 91)( 19, 90)( 20, 92)( 21,106)( 22,105)( 23,107)( 24,103)( 25,102)( 26,104)( 27,109)( 28,108)( 29,110)( 30, 97)( 31, 96)( 32, 98)( 33, 94)( 34, 93)( 35, 95)( 36,100)( 37, 99)( 38,101)( 39,133)( 40,132)( 41,134)( 42,130)( 43,129)( 44,131)( 45,136)( 46,135)( 47,137)( 48,142)( 49,141)( 50,143)( 51,139)( 52,138)( 53,140)( 54,145)( 55,144)( 56,146)( 57,115)( 58,114)( 59,116)( 60,112)( 61,111)( 62,113)( 63,118)( 64,117)( 65,119)( 66,124)( 67,123)( 68,125)( 69,121)( 70,120)( 71,122)( 72,127)( 73,126)( 74,128);; s3 := ( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)( 49, 50)( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)( 73, 74)( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 88, 89)( 91, 92)( 94, 95)( 97, 98)(100,101)(103,104)(106,107)(109,110)(112,113)(115,116)(118,119)(121,122)(124,125)(127,128)(130,131)(133,134)(136,137)(139,140)(142,143)(145,146);; 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,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(146)!(1,2); s1 := Sym(146)!( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)( 21, 30)( 22, 32)( 23, 31)( 24, 36)( 25, 38)( 26, 37)( 27, 33)( 28, 35)( 29, 34)( 39, 57)( 40, 59)( 41, 58)( 42, 63)( 43, 65)( 44, 64)( 45, 60)( 46, 62)( 47, 61)( 48, 66)( 49, 68)( 50, 67)( 51, 72)( 52, 74)( 53, 73)( 54, 69)( 55, 71)( 56, 70)( 75,111)( 76,113)( 77,112)( 78,117)( 79,119)( 80,118)( 81,114)( 82,116)( 83,115)( 84,120)( 85,122)( 86,121)( 87,126)( 88,128)( 89,127)( 90,123)( 91,125)( 92,124)( 93,138)( 94,140)( 95,139)( 96,144)( 97,146)( 98,145)( 99,141)(100,143)(101,142)(102,129)(103,131)(104,130)(105,135)(106,137)(107,136)(108,132)(109,134)(110,133); s2 := Sym(146)!( 3, 79)( 4, 78)( 5, 80)( 6, 76)( 7, 75)( 8, 77)( 9, 82)( 10, 81)( 11, 83)( 12, 88)( 13, 87)( 14, 89)( 15, 85)( 16, 84)( 17, 86)( 18, 91)( 19, 90)( 20, 92)( 21,106)( 22,105)( 23,107)( 24,103)( 25,102)( 26,104)( 27,109)( 28,108)( 29,110)( 30, 97)( 31, 96)( 32, 98)( 33, 94)( 34, 93)( 35, 95)( 36,100)( 37, 99)( 38,101)( 39,133)( 40,132)( 41,134)( 42,130)( 43,129)( 44,131)( 45,136)( 46,135)( 47,137)( 48,142)( 49,141)( 50,143)( 51,139)( 52,138)( 53,140)( 54,145)( 55,144)( 56,146)( 57,115)( 58,114)( 59,116)( 60,112)( 61,111)( 62,113)( 63,118)( 64,117)( 65,119)( 66,124)( 67,123)( 68,125)( 69,121)( 70,120)( 71,122)( 72,127)( 73,126)( 74,128); s3 := Sym(146)!( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)( 49, 50)( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)( 73, 74)( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 88, 89)( 91, 92)( 94, 95)( 97, 98)(100,101)(103,104)(106,107)(109,110)(112,113)(115,116)(118,119)(121,122)(124,125)(127,128)(130,131)(133,134)(136,137)(139,140)(142,143)(145,146); poly := sub<Sym(146)|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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;