Overview
- Group
- SmallGroup(1152,154283)
- Rank
- 4
- Schläfli Type
- {18,8,2}
- Vertices, edges, …
- 36, 144, 16, 2
- Order of s0s1s2s3
- 18
- 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
3-fold
4-fold
8-fold
12-fold
24-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 10)( 6, 9)( 7, 11)( 8, 12)( 15, 16)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 42)( 22, 41)( 23, 43)( 24, 44)( 25, 38)( 26, 37)( 27, 39)( 28, 40)( 29, 45)( 30, 46)( 31, 48)( 32, 47)( 49,113)( 50,114)( 51,116)( 52,115)( 53,122)( 54,121)( 55,123)( 56,124)( 57,118)( 58,117)( 59,119)( 60,120)( 61,125)( 62,126)( 63,128)( 64,127)( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69,106)( 70,105)( 71,107)( 72,108)( 73,102)( 74,101)( 75,103)( 76,104)( 77,109)( 78,110)( 79,112)( 80,111)( 81,129)( 82,130)( 83,132)( 84,131)( 85,138)( 86,137)( 87,139)( 88,140)( 89,134)( 90,133)( 91,135)( 92,136)( 93,141)( 94,142)( 95,144)( 96,143);; s1 := ( 1, 49)( 2, 51)( 3, 50)( 4, 52)( 5, 56)( 6, 54)( 7, 55)( 8, 53)( 9, 64)( 10, 62)( 11, 63)( 12, 61)( 13, 60)( 14, 58)( 15, 59)( 16, 57)( 17, 81)( 18, 83)( 19, 82)( 20, 84)( 21, 88)( 22, 86)( 23, 87)( 24, 85)( 25, 96)( 26, 94)( 27, 95)( 28, 93)( 29, 92)( 30, 90)( 31, 91)( 32, 89)( 33, 65)( 34, 67)( 35, 66)( 36, 68)( 37, 72)( 38, 70)( 39, 71)( 40, 69)( 41, 80)( 42, 78)( 43, 79)( 44, 77)( 45, 76)( 46, 74)( 47, 75)( 48, 73)( 97,113)( 98,115)( 99,114)(100,116)(101,120)(102,118)(103,119)(104,117)(105,128)(106,126)(107,127)(108,125)(109,124)(110,122)(111,123)(112,121)(130,131)(133,136)(137,144)(138,142)(139,143)(140,141);; s2 := ( 1, 13)( 2, 14)( 3, 15)( 4, 16)( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 33, 45)( 34, 46)( 35, 47)( 36, 48)( 37, 41)( 38, 42)( 39, 43)( 40, 44)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)( 81, 93)( 82, 94)( 83, 95)( 84, 96)( 85, 89)( 86, 90)( 87, 91)( 88, 92)( 97,109)( 98,110)( 99,111)(100,112)(101,105)(102,106)(103,107)(104,108)(113,125)(114,126)(115,127)(116,128)(117,121)(118,122)(119,123)(120,124)(129,141)(130,142)(131,143)(132,144)(133,137)(134,138)(135,139)(136,140);; s3 := (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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(146)!( 3, 4)( 5, 10)( 6, 9)( 7, 11)( 8, 12)( 15, 16)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 42)( 22, 41)( 23, 43)( 24, 44)( 25, 38)( 26, 37)( 27, 39)( 28, 40)( 29, 45)( 30, 46)( 31, 48)( 32, 47)( 49,113)( 50,114)( 51,116)( 52,115)( 53,122)( 54,121)( 55,123)( 56,124)( 57,118)( 58,117)( 59,119)( 60,120)( 61,125)( 62,126)( 63,128)( 64,127)( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69,106)( 70,105)( 71,107)( 72,108)( 73,102)( 74,101)( 75,103)( 76,104)( 77,109)( 78,110)( 79,112)( 80,111)( 81,129)( 82,130)( 83,132)( 84,131)( 85,138)( 86,137)( 87,139)( 88,140)( 89,134)( 90,133)( 91,135)( 92,136)( 93,141)( 94,142)( 95,144)( 96,143); s1 := Sym(146)!( 1, 49)( 2, 51)( 3, 50)( 4, 52)( 5, 56)( 6, 54)( 7, 55)( 8, 53)( 9, 64)( 10, 62)( 11, 63)( 12, 61)( 13, 60)( 14, 58)( 15, 59)( 16, 57)( 17, 81)( 18, 83)( 19, 82)( 20, 84)( 21, 88)( 22, 86)( 23, 87)( 24, 85)( 25, 96)( 26, 94)( 27, 95)( 28, 93)( 29, 92)( 30, 90)( 31, 91)( 32, 89)( 33, 65)( 34, 67)( 35, 66)( 36, 68)( 37, 72)( 38, 70)( 39, 71)( 40, 69)( 41, 80)( 42, 78)( 43, 79)( 44, 77)( 45, 76)( 46, 74)( 47, 75)( 48, 73)( 97,113)( 98,115)( 99,114)(100,116)(101,120)(102,118)(103,119)(104,117)(105,128)(106,126)(107,127)(108,125)(109,124)(110,122)(111,123)(112,121)(130,131)(133,136)(137,144)(138,142)(139,143)(140,141); s2 := Sym(146)!( 1, 13)( 2, 14)( 3, 15)( 4, 16)( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 33, 45)( 34, 46)( 35, 47)( 36, 48)( 37, 41)( 38, 42)( 39, 43)( 40, 44)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)( 81, 93)( 82, 94)( 83, 95)( 84, 96)( 85, 89)( 86, 90)( 87, 91)( 88, 92)( 97,109)( 98,110)( 99,111)(100,112)(101,105)(102,106)(103,107)(104,108)(113,125)(114,126)(115,127)(116,128)(117,121)(118,122)(119,123)(120,124)(129,141)(130,142)(131,143)(132,144)(133,137)(134,138)(135,139)(136,140); s3 := Sym(146)!(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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;