Overview
- Group
- SmallGroup(1152,157559)
- Rank
- 4
- Schläfli Type
- {6,6,4}
- Vertices, edges, …
- 6, 72, 48, 16
- 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*s2*s3*s2*s1*s3*s2> of order 2
8 facets
- 8 of {6,6}*72b
6 vertex figures
- 6 of 2-fold non-regular quotient of {6,4}*192b
P/N, where N=<s1*s2*s3*s2*s1*(s2*s3)^2> of order 2
8 facets
- 8 of {6,6}*72b
6 vertex figures
- 6 of 2-fold non-regular quotient of {6,4}*192b
P/N, where N=<(s1*s2*s3*s2)^2> of order 2
8 facets
- 8 of {6,6}*72b
6 vertex figures
- 6 of 2-fold non-regular quotient of {6,4}*192b
P/N, where N=<(s1*s2)^3> of order 2
12 facets
6 vertex figures
- 6 of 2-fold non-regular quotient of {6,4}*192b
P/N, where N=<(s2*s3)^2, s1*s2*s3*s2*s1*s3> of order 4
4 facets
- 4 of {6,6}*72b
6 vertex figures
- 6 of 4-fold non-regular quotient of {6,4}*192b
P/N, where N=<(s1*s2)^3, s1*(s2*s1*s3)^2*s2> of order 4
6 facets
6 vertex figures
- 6 of 4-fold non-regular quotient of {6,4}*192b
Representations
Permutation Representation (GAP)
s0 := ( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)( 92, 96)(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)(116,120)(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)(140,144);; s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 11, 12)( 13, 29)( 14, 30)( 15, 32)( 16, 31)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 47, 48)( 49, 65)( 50, 66)( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 73, 77)( 74, 78)( 75, 80)( 76, 79)( 83, 84)( 85,101)( 86,102)( 87,104)( 88,103)( 89, 97)( 90, 98)( 91,100)( 92, 99)( 93,105)( 94,106)( 95,108)( 96,107)(109,113)(110,114)(111,116)(112,115)(119,120)(121,137)(122,138)(123,140)(124,139)(125,133)(126,134)(127,136)(128,135)(129,141)(130,142)(131,144)(132,143);; s2 := ( 1, 13)( 2, 16)( 3, 15)( 4, 14)( 5, 21)( 6, 24)( 7, 23)( 8, 22)( 9, 17)( 10, 20)( 11, 19)( 12, 18)( 26, 28)( 29, 33)( 30, 36)( 31, 35)( 32, 34)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)( 43, 59)( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 62, 64)( 65, 69)( 66, 72)( 67, 71)( 68, 70)( 73,121)( 74,124)( 75,123)( 76,122)( 77,129)( 78,132)( 79,131)( 80,130)( 81,125)( 82,128)( 83,127)( 84,126)( 85,109)( 86,112)( 87,111)( 88,110)( 89,117)( 90,120)( 91,119)( 92,118)( 93,113)( 94,116)( 95,115)( 96,114)( 97,133)( 98,136)( 99,135)(100,134)(101,141)(102,144)(103,143)(104,142)(105,137)(106,140)(107,139)(108,138);; s3 := ( 1, 74)( 2, 73)( 3, 76)( 4, 75)( 5, 78)( 6, 77)( 7, 80)( 8, 79)( 9, 82)( 10, 81)( 11, 84)( 12, 83)( 13, 86)( 14, 85)( 15, 88)( 16, 87)( 17, 90)( 18, 89)( 19, 92)( 20, 91)( 21, 94)( 22, 93)( 23, 96)( 24, 95)( 25, 98)( 26, 97)( 27,100)( 28, 99)( 29,102)( 30,101)( 31,104)( 32,103)( 33,106)( 34,105)( 35,108)( 36,107)( 37,110)( 38,109)( 39,112)( 40,111)( 41,114)( 42,113)( 43,116)( 44,115)( 45,118)( 46,117)( 47,120)( 48,119)( 49,122)( 50,121)( 51,124)( 52,123)( 53,126)( 54,125)( 55,128)( 56,127)( 57,130)( 58,129)( 59,132)( 60,131)( 61,134)( 62,133)( 63,136)( 64,135)( 65,138)( 66,137)( 67,140)( 68,139)( 69,142)( 70,141)( 71,144)( 72,143);; 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*s3*s2*s3,
s0*s1*s2*s0*s1*s0*s1*s2*s0*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*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(144)!( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)( 92, 96)(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)(116,120)(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)(140,144); s1 := Sym(144)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 11, 12)( 13, 29)( 14, 30)( 15, 32)( 16, 31)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 47, 48)( 49, 65)( 50, 66)( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 73, 77)( 74, 78)( 75, 80)( 76, 79)( 83, 84)( 85,101)( 86,102)( 87,104)( 88,103)( 89, 97)( 90, 98)( 91,100)( 92, 99)( 93,105)( 94,106)( 95,108)( 96,107)(109,113)(110,114)(111,116)(112,115)(119,120)(121,137)(122,138)(123,140)(124,139)(125,133)(126,134)(127,136)(128,135)(129,141)(130,142)(131,144)(132,143); s2 := Sym(144)!( 1, 13)( 2, 16)( 3, 15)( 4, 14)( 5, 21)( 6, 24)( 7, 23)( 8, 22)( 9, 17)( 10, 20)( 11, 19)( 12, 18)( 26, 28)( 29, 33)( 30, 36)( 31, 35)( 32, 34)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)( 43, 59)( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 62, 64)( 65, 69)( 66, 72)( 67, 71)( 68, 70)( 73,121)( 74,124)( 75,123)( 76,122)( 77,129)( 78,132)( 79,131)( 80,130)( 81,125)( 82,128)( 83,127)( 84,126)( 85,109)( 86,112)( 87,111)( 88,110)( 89,117)( 90,120)( 91,119)( 92,118)( 93,113)( 94,116)( 95,115)( 96,114)( 97,133)( 98,136)( 99,135)(100,134)(101,141)(102,144)(103,143)(104,142)(105,137)(106,140)(107,139)(108,138); s3 := Sym(144)!( 1, 74)( 2, 73)( 3, 76)( 4, 75)( 5, 78)( 6, 77)( 7, 80)( 8, 79)( 9, 82)( 10, 81)( 11, 84)( 12, 83)( 13, 86)( 14, 85)( 15, 88)( 16, 87)( 17, 90)( 18, 89)( 19, 92)( 20, 91)( 21, 94)( 22, 93)( 23, 96)( 24, 95)( 25, 98)( 26, 97)( 27,100)( 28, 99)( 29,102)( 30,101)( 31,104)( 32,103)( 33,106)( 34,105)( 35,108)( 36,107)( 37,110)( 38,109)( 39,112)( 40,111)( 41,114)( 42,113)( 43,116)( 44,115)( 45,118)( 46,117)( 47,120)( 48,119)( 49,122)( 50,121)( 51,124)( 52,123)( 53,126)( 54,125)( 55,128)( 56,127)( 57,130)( 58,129)( 59,132)( 60,131)( 61,134)( 62,133)( 63,136)( 64,135)( 65,138)( 66,137)( 67,140)( 68,139)( 69,142)( 70,141)( 71,144)( 72,143); 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, s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s0*s1*s0*s1*s2*s0*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*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2 >;
References
None.
to this polytope.