Overview
- Group
- SmallGroup(1152,157621)
- Rank
- 4
- Schläfli Type
- {6,6,8}
- Vertices, edges, …
- 6, 36, 48, 16
- Order of s0s1s2s3
- 6
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
24-fold
48-fold
72-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 := ( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144);; s1 := ( 1, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 15)( 6, 16)( 7, 13)( 8, 14)( 19, 20)( 21, 23)( 22, 24)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 63)( 30, 64)( 31, 61)( 32, 62)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 55)( 38, 56)( 39, 53)( 40, 54)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)( 46, 72)( 47, 69)( 48, 70)( 73, 82)( 74, 81)( 75, 83)( 76, 84)( 77, 88)( 78, 87)( 79, 86)( 80, 85)( 89, 90)( 93, 96)( 94, 95)( 97,130)( 98,129)( 99,131)(100,132)(101,136)(102,135)(103,134)(104,133)(105,122)(106,121)(107,123)(108,124)(109,128)(110,127)(111,126)(112,125)(113,138)(114,137)(115,139)(116,140)(117,144)(118,143)(119,142)(120,141);; s2 := ( 1, 25)( 2, 26)( 3, 31)( 4, 32)( 5, 30)( 6, 29)( 7, 27)( 8, 28)( 9, 33)( 10, 34)( 11, 39)( 12, 40)( 13, 38)( 14, 37)( 15, 35)( 16, 36)( 17, 41)( 18, 42)( 19, 47)( 20, 48)( 21, 46)( 22, 45)( 23, 43)( 24, 44)( 51, 55)( 52, 56)( 53, 54)( 59, 63)( 60, 64)( 61, 62)( 67, 71)( 68, 72)( 69, 70)( 73, 97)( 74, 98)( 75,103)( 76,104)( 77,102)( 78,101)( 79, 99)( 80,100)( 81,105)( 82,106)( 83,111)( 84,112)( 85,110)( 86,109)( 87,107)( 88,108)( 89,113)( 90,114)( 91,119)( 92,120)( 93,118)( 94,117)( 95,115)( 96,116)(123,127)(124,128)(125,126)(131,135)(132,136)(133,134)(139,143)(140,144)(141,142);; s3 := ( 1, 75)( 2, 76)( 3, 74)( 4, 73)( 5, 79)( 6, 80)( 7, 78)( 8, 77)( 9, 83)( 10, 84)( 11, 82)( 12, 81)( 13, 87)( 14, 88)( 15, 86)( 16, 85)( 17, 91)( 18, 92)( 19, 90)( 20, 89)( 21, 95)( 22, 96)( 23, 94)( 24, 93)( 25, 99)( 26,100)( 27, 98)( 28, 97)( 29,103)( 30,104)( 31,102)( 32,101)( 33,107)( 34,108)( 35,106)( 36,105)( 37,111)( 38,112)( 39,110)( 40,109)( 41,115)( 42,116)( 43,114)( 44,113)( 45,119)( 46,120)( 47,118)( 48,117)( 49,123)( 50,124)( 51,122)( 52,121)( 53,127)( 54,128)( 55,126)( 56,125)( 57,131)( 58,132)( 59,130)( 60,129)( 61,135)( 62,136)( 63,134)( 64,133)( 65,139)( 66,140)( 67,138)( 68,137)( 69,143)( 70,144)( 71,142)( 72,141);; 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*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(144)!( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144); s1 := Sym(144)!( 1, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 15)( 6, 16)( 7, 13)( 8, 14)( 19, 20)( 21, 23)( 22, 24)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 63)( 30, 64)( 31, 61)( 32, 62)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 55)( 38, 56)( 39, 53)( 40, 54)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)( 46, 72)( 47, 69)( 48, 70)( 73, 82)( 74, 81)( 75, 83)( 76, 84)( 77, 88)( 78, 87)( 79, 86)( 80, 85)( 89, 90)( 93, 96)( 94, 95)( 97,130)( 98,129)( 99,131)(100,132)(101,136)(102,135)(103,134)(104,133)(105,122)(106,121)(107,123)(108,124)(109,128)(110,127)(111,126)(112,125)(113,138)(114,137)(115,139)(116,140)(117,144)(118,143)(119,142)(120,141); s2 := Sym(144)!( 1, 25)( 2, 26)( 3, 31)( 4, 32)( 5, 30)( 6, 29)( 7, 27)( 8, 28)( 9, 33)( 10, 34)( 11, 39)( 12, 40)( 13, 38)( 14, 37)( 15, 35)( 16, 36)( 17, 41)( 18, 42)( 19, 47)( 20, 48)( 21, 46)( 22, 45)( 23, 43)( 24, 44)( 51, 55)( 52, 56)( 53, 54)( 59, 63)( 60, 64)( 61, 62)( 67, 71)( 68, 72)( 69, 70)( 73, 97)( 74, 98)( 75,103)( 76,104)( 77,102)( 78,101)( 79, 99)( 80,100)( 81,105)( 82,106)( 83,111)( 84,112)( 85,110)( 86,109)( 87,107)( 88,108)( 89,113)( 90,114)( 91,119)( 92,120)( 93,118)( 94,117)( 95,115)( 96,116)(123,127)(124,128)(125,126)(131,135)(132,136)(133,134)(139,143)(140,144)(141,142); s3 := Sym(144)!( 1, 75)( 2, 76)( 3, 74)( 4, 73)( 5, 79)( 6, 80)( 7, 78)( 8, 77)( 9, 83)( 10, 84)( 11, 82)( 12, 81)( 13, 87)( 14, 88)( 15, 86)( 16, 85)( 17, 91)( 18, 92)( 19, 90)( 20, 89)( 21, 95)( 22, 96)( 23, 94)( 24, 93)( 25, 99)( 26,100)( 27, 98)( 28, 97)( 29,103)( 30,104)( 31,102)( 32,101)( 33,107)( 34,108)( 35,106)( 36,105)( 37,111)( 38,112)( 39,110)( 40,109)( 41,115)( 42,116)( 43,114)( 44,113)( 45,119)( 46,120)( 47,118)( 48,117)( 49,123)( 50,124)( 51,122)( 52,121)( 53,127)( 54,128)( 55,126)( 56,125)( 57,131)( 58,132)( 59,130)( 60,129)( 61,135)( 62,136)( 63,134)( 64,133)( 65,139)( 66,140)( 67,138)( 68,137)( 69,143)( 70,144)( 71,142)( 72,141); poly := sub<Sym(144)|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*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s3*s2 >;
References
None.
to this polytope.