Overview
- Group
- SmallGroup(1152,98777)
- Rank
- 4
- Schläfli Type
- {2,36,8}
- Vertices, edges, …
- 2, 36, 144, 8
- Order of s0s1s2s3
- 72
- 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, 10)( 7, 9)( 8, 11)( 13, 14)( 15, 19)( 16, 18)( 17, 20)( 21, 30)( 22, 32)( 23, 31)( 24, 37)( 25, 36)( 26, 38)( 27, 34)( 28, 33)( 29, 35)( 40, 41)( 42, 46)( 43, 45)( 44, 47)( 49, 50)( 51, 55)( 52, 54)( 53, 56)( 57, 66)( 58, 68)( 59, 67)( 60, 73)( 61, 72)( 62, 74)( 63, 70)( 64, 69)( 65, 71)( 75,111)( 76,113)( 77,112)( 78,118)( 79,117)( 80,119)( 81,115)( 82,114)( 83,116)( 84,120)( 85,122)( 86,121)( 87,127)( 88,126)( 89,128)( 90,124)( 91,123)( 92,125)( 93,138)( 94,140)( 95,139)( 96,145)( 97,144)( 98,146)( 99,142)(100,141)(101,143)(102,129)(103,131)(104,130)(105,136)(106,135)(107,137)(108,133)(109,132)(110,134);; s2 := ( 3, 78)( 4, 80)( 5, 79)( 6, 75)( 7, 77)( 8, 76)( 9, 82)( 10, 81)( 11, 83)( 12, 87)( 13, 89)( 14, 88)( 15, 84)( 16, 86)( 17, 85)( 18, 91)( 19, 90)( 20, 92)( 21,105)( 22,107)( 23,106)( 24,102)( 25,104)( 26,103)( 27,109)( 28,108)( 29,110)( 30, 96)( 31, 98)( 32, 97)( 33, 93)( 34, 95)( 35, 94)( 36,100)( 37, 99)( 38,101)( 39,114)( 40,116)( 41,115)( 42,111)( 43,113)( 44,112)( 45,118)( 46,117)( 47,119)( 48,123)( 49,125)( 50,124)( 51,120)( 52,122)( 53,121)( 54,127)( 55,126)( 56,128)( 57,141)( 58,143)( 59,142)( 60,138)( 61,140)( 62,139)( 63,145)( 64,144)( 65,146)( 66,132)( 67,134)( 68,133)( 69,129)( 70,131)( 71,130)( 72,136)( 73,135)( 74,137);; s3 := ( 21, 30)( 22, 31)( 23, 32)( 24, 33)( 25, 34)( 26, 35)( 27, 36)( 28, 37)( 29, 38)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)( 45, 54)( 46, 55)( 47, 56)( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)( 81, 99)( 82,100)( 83,101)( 84,102)( 85,103)( 86,104)( 87,105)( 88,106)( 89,107)( 90,108)( 91,109)( 92,110)(111,138)(112,139)(113,140)(114,141)(115,142)(116,143)(117,144)(118,145)(119,146)(120,129)(121,130)(122,131)(123,132)(124,133)(125,134)(126,135)(127,136)(128,137);; 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*s1*s2*s3*s2*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(146)!(1,2); s1 := Sym(146)!( 4, 5)( 6, 10)( 7, 9)( 8, 11)( 13, 14)( 15, 19)( 16, 18)( 17, 20)( 21, 30)( 22, 32)( 23, 31)( 24, 37)( 25, 36)( 26, 38)( 27, 34)( 28, 33)( 29, 35)( 40, 41)( 42, 46)( 43, 45)( 44, 47)( 49, 50)( 51, 55)( 52, 54)( 53, 56)( 57, 66)( 58, 68)( 59, 67)( 60, 73)( 61, 72)( 62, 74)( 63, 70)( 64, 69)( 65, 71)( 75,111)( 76,113)( 77,112)( 78,118)( 79,117)( 80,119)( 81,115)( 82,114)( 83,116)( 84,120)( 85,122)( 86,121)( 87,127)( 88,126)( 89,128)( 90,124)( 91,123)( 92,125)( 93,138)( 94,140)( 95,139)( 96,145)( 97,144)( 98,146)( 99,142)(100,141)(101,143)(102,129)(103,131)(104,130)(105,136)(106,135)(107,137)(108,133)(109,132)(110,134); s2 := Sym(146)!( 3, 78)( 4, 80)( 5, 79)( 6, 75)( 7, 77)( 8, 76)( 9, 82)( 10, 81)( 11, 83)( 12, 87)( 13, 89)( 14, 88)( 15, 84)( 16, 86)( 17, 85)( 18, 91)( 19, 90)( 20, 92)( 21,105)( 22,107)( 23,106)( 24,102)( 25,104)( 26,103)( 27,109)( 28,108)( 29,110)( 30, 96)( 31, 98)( 32, 97)( 33, 93)( 34, 95)( 35, 94)( 36,100)( 37, 99)( 38,101)( 39,114)( 40,116)( 41,115)( 42,111)( 43,113)( 44,112)( 45,118)( 46,117)( 47,119)( 48,123)( 49,125)( 50,124)( 51,120)( 52,122)( 53,121)( 54,127)( 55,126)( 56,128)( 57,141)( 58,143)( 59,142)( 60,138)( 61,140)( 62,139)( 63,145)( 64,144)( 65,146)( 66,132)( 67,134)( 68,133)( 69,129)( 70,131)( 71,130)( 72,136)( 73,135)( 74,137); s3 := Sym(146)!( 21, 30)( 22, 31)( 23, 32)( 24, 33)( 25, 34)( 26, 35)( 27, 36)( 28, 37)( 29, 38)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)( 45, 54)( 46, 55)( 47, 56)( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)( 81, 99)( 82,100)( 83,101)( 84,102)( 85,103)( 86,104)( 87,105)( 88,106)( 89,107)( 90,108)( 91,109)( 92,110)(111,138)(112,139)(113,140)(114,141)(115,142)(116,143)(117,144)(118,145)(119,146)(120,129)(121,130)(122,131)(123,132)(124,133)(125,134)(126,135)(127,136)(128,137); 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*s1*s2*s3*s2*s1*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 >;