Overview
- Group
- SmallGroup(1152,157559)
- Rank
- 4
- Schläfli Type
- {4,6,6}
- Vertices, edges, …
- 4, 48, 72, 24
- Order of s0s1s2s3
- 12
- 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
16-fold
24-fold
36-fold
48-fold
72-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<s2*s1*(s3*s2)^2*s1*s3*s2*s3> of order 2
12 facets
- 12 of {4,6}*48a
4 vertex figures
- 4 of 2-fold non-regular quotient of {6,6}*288b
P/N, where N=<s2*s1*(s2*s3)^2*s2*s1*s3*s2> of order 2
12 facets
- 12 of {4,6}*48a
4 vertex figures
- 4 of 2-fold non-regular quotient of {6,6}*288b
P/N, where N=<s1*(s3*s2)^2*s1*(s2*s3)^2> of order 3
8 facets
- 8 of {4,6}*48a
4 vertex figures
- 4 of 3-fold non-regular quotient of {6,6}*288b
P/N, where N=<s1*s2*s3*s2*s1*(s3*s2)^2> of order 4
6 facets
- 6 of {4,6}*48a
4 vertex figures
- 4 of 4-fold non-regular quotient of {6,6}*288b
Representations
Permutation Representation (GAP)
s0 := ( 73,109)( 74,110)( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)( 80,116)( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)( 88,124)( 89,125)( 90,126)( 91,127)( 92,128)( 93,129)( 94,130)( 95,131)( 96,132)( 97,133)( 98,134)( 99,135)(100,136)(101,137)(102,138)(103,139)(104,140)(105,141)(106,142)(107,143)(108,144);; s1 := ( 1, 73)( 2, 74)( 3, 76)( 4, 75)( 5, 81)( 6, 82)( 7, 84)( 8, 83)( 9, 77)( 10, 78)( 11, 80)( 12, 79)( 13, 97)( 14, 98)( 15,100)( 16, 99)( 17,105)( 18,106)( 19,108)( 20,107)( 21,101)( 22,102)( 23,104)( 24,103)( 25, 85)( 26, 86)( 27, 88)( 28, 87)( 29, 93)( 30, 94)( 31, 96)( 32, 95)( 33, 89)( 34, 90)( 35, 92)( 36, 91)( 37,109)( 38,110)( 39,112)( 40,111)( 41,117)( 42,118)( 43,120)( 44,119)( 45,113)( 46,114)( 47,116)( 48,115)( 49,133)( 50,134)( 51,136)( 52,135)( 53,141)( 54,142)( 55,144)( 56,143)( 57,137)( 58,138)( 59,140)( 60,139)( 61,121)( 62,122)( 63,124)( 64,123)( 65,129)( 66,130)( 67,132)( 68,131)( 69,125)( 70,126)( 71,128)( 72,127);; s2 := ( 1, 17)( 2, 20)( 3, 19)( 4, 18)( 5, 13)( 6, 16)( 7, 15)( 8, 14)( 9, 21)( 10, 24)( 11, 23)( 12, 22)( 25, 29)( 26, 32)( 27, 31)( 28, 30)( 34, 36)( 37, 53)( 38, 56)( 39, 55)( 40, 54)( 41, 49)( 42, 52)( 43, 51)( 44, 50)( 45, 57)( 46, 60)( 47, 59)( 48, 58)( 61, 65)( 62, 68)( 63, 67)( 64, 66)( 70, 72)( 73, 89)( 74, 92)( 75, 91)( 76, 90)( 77, 85)( 78, 88)( 79, 87)( 80, 86)( 81, 93)( 82, 96)( 83, 95)( 84, 94)( 97,101)( 98,104)( 99,103)(100,102)(106,108)(109,125)(110,128)(111,127)(112,126)(113,121)(114,124)(115,123)(116,122)(117,129)(118,132)(119,131)(120,130)(133,137)(134,140)(135,139)(136,138)(142,144);; s3 := ( 1, 2)( 5, 6)( 9, 10)( 13, 26)( 14, 25)( 15, 27)( 16, 28)( 17, 30)( 18, 29)( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 23, 35)( 24, 36)( 37, 38)( 41, 42)( 45, 46)( 49, 62)( 50, 61)( 51, 63)( 52, 64)( 53, 66)( 54, 65)( 55, 67)( 56, 68)( 57, 70)( 58, 69)( 59, 71)( 60, 72)( 73, 74)( 77, 78)( 81, 82)( 85, 98)( 86, 97)( 87, 99)( 88,100)( 89,102)( 90,101)( 91,103)( 92,104)( 93,106)( 94,105)( 95,107)( 96,108)(109,110)(113,114)(117,118)(121,134)(122,133)(123,135)(124,136)(125,138)(126,137)(127,139)(128,140)(129,142)(130,141)(131,143)(132,144);; 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(144)!( 73,109)( 74,110)( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)( 80,116)( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)( 88,124)( 89,125)( 90,126)( 91,127)( 92,128)( 93,129)( 94,130)( 95,131)( 96,132)( 97,133)( 98,134)( 99,135)(100,136)(101,137)(102,138)(103,139)(104,140)(105,141)(106,142)(107,143)(108,144); s1 := Sym(144)!( 1, 73)( 2, 74)( 3, 76)( 4, 75)( 5, 81)( 6, 82)( 7, 84)( 8, 83)( 9, 77)( 10, 78)( 11, 80)( 12, 79)( 13, 97)( 14, 98)( 15,100)( 16, 99)( 17,105)( 18,106)( 19,108)( 20,107)( 21,101)( 22,102)( 23,104)( 24,103)( 25, 85)( 26, 86)( 27, 88)( 28, 87)( 29, 93)( 30, 94)( 31, 96)( 32, 95)( 33, 89)( 34, 90)( 35, 92)( 36, 91)( 37,109)( 38,110)( 39,112)( 40,111)( 41,117)( 42,118)( 43,120)( 44,119)( 45,113)( 46,114)( 47,116)( 48,115)( 49,133)( 50,134)( 51,136)( 52,135)( 53,141)( 54,142)( 55,144)( 56,143)( 57,137)( 58,138)( 59,140)( 60,139)( 61,121)( 62,122)( 63,124)( 64,123)( 65,129)( 66,130)( 67,132)( 68,131)( 69,125)( 70,126)( 71,128)( 72,127); s2 := Sym(144)!( 1, 17)( 2, 20)( 3, 19)( 4, 18)( 5, 13)( 6, 16)( 7, 15)( 8, 14)( 9, 21)( 10, 24)( 11, 23)( 12, 22)( 25, 29)( 26, 32)( 27, 31)( 28, 30)( 34, 36)( 37, 53)( 38, 56)( 39, 55)( 40, 54)( 41, 49)( 42, 52)( 43, 51)( 44, 50)( 45, 57)( 46, 60)( 47, 59)( 48, 58)( 61, 65)( 62, 68)( 63, 67)( 64, 66)( 70, 72)( 73, 89)( 74, 92)( 75, 91)( 76, 90)( 77, 85)( 78, 88)( 79, 87)( 80, 86)( 81, 93)( 82, 96)( 83, 95)( 84, 94)( 97,101)( 98,104)( 99,103)(100,102)(106,108)(109,125)(110,128)(111,127)(112,126)(113,121)(114,124)(115,123)(116,122)(117,129)(118,132)(119,131)(120,130)(133,137)(134,140)(135,139)(136,138)(142,144); s3 := Sym(144)!( 1, 2)( 5, 6)( 9, 10)( 13, 26)( 14, 25)( 15, 27)( 16, 28)( 17, 30)( 18, 29)( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 23, 35)( 24, 36)( 37, 38)( 41, 42)( 45, 46)( 49, 62)( 50, 61)( 51, 63)( 52, 64)( 53, 66)( 54, 65)( 55, 67)( 56, 68)( 57, 70)( 58, 69)( 59, 71)( 60, 72)( 73, 74)( 77, 78)( 81, 82)( 85, 98)( 86, 97)( 87, 99)( 88,100)( 89,102)( 90,101)( 91,103)( 92,104)( 93,106)( 94,105)( 95,107)( 96,108)(109,110)(113,114)(117,118)(121,134)(122,133)(123,135)(124,136)(125,138)(126,137)(127,139)(128,140)(129,142)(130,141)(131,143)(132,144); 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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >;
References
None.
to this polytope.