Overview
- Group
- SmallGroup(1152,157582)
- Rank
- 4
- Schläfli Type
- {6,6,2}
- Vertices, edges, …
- 48, 144, 48, 2
- Order of s0s1s2s3
- 24
- 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
12-fold
16-fold
24-fold
48-fold
72-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 1, 73)( 2, 74)( 3, 78)( 4, 77)( 5, 76)( 6, 75)( 7, 80)( 8, 79)( 9, 89)( 10, 90)( 11, 94)( 12, 93)( 13, 92)( 14, 91)( 15, 96)( 16, 95)( 17, 81)( 18, 82)( 19, 86)( 20, 85)( 21, 84)( 22, 83)( 23, 88)( 24, 87)( 25,121)( 26,122)( 27,126)( 28,125)( 29,124)( 30,123)( 31,128)( 32,127)( 33,137)( 34,138)( 35,142)( 36,141)( 37,140)( 38,139)( 39,144)( 40,143)( 41,129)( 42,130)( 43,134)( 44,133)( 45,132)( 46,131)( 47,136)( 48,135)( 49, 97)( 50, 98)( 51,102)( 52,101)( 53,100)( 54, 99)( 55,104)( 56,103)( 57,113)( 58,114)( 59,118)( 60,117)( 61,116)( 62,115)( 63,120)( 64,119)( 65,105)( 66,106)( 67,110)( 68,109)( 69,108)( 70,107)( 71,112)( 72,111);; s1 := ( 1, 33)( 2, 34)( 3, 36)( 4, 35)( 5, 39)( 6, 40)( 7, 37)( 8, 38)( 9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 31)( 14, 32)( 15, 29)( 16, 30)( 17, 41)( 18, 42)( 19, 44)( 20, 43)( 21, 47)( 22, 48)( 23, 45)( 24, 46)( 49, 57)( 50, 58)( 51, 60)( 52, 59)( 53, 63)( 54, 64)( 55, 61)( 56, 62)( 67, 68)( 69, 71)( 70, 72)( 73,105)( 74,106)( 75,108)( 76,107)( 77,111)( 78,112)( 79,109)( 80,110)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,103)( 86,104)( 87,101)( 88,102)( 89,113)( 90,114)( 91,116)( 92,115)( 93,119)( 94,120)( 95,117)( 96,118)(121,129)(122,130)(123,132)(124,131)(125,135)(126,136)(127,133)(128,134)(139,140)(141,143)(142,144);; s2 := ( 1, 7)( 2, 8)( 5, 6)( 9, 15)( 10, 16)( 13, 14)( 17, 23)( 18, 24)( 21, 22)( 25, 55)( 26, 56)( 27, 51)( 28, 52)( 29, 54)( 30, 53)( 31, 49)( 32, 50)( 33, 63)( 34, 64)( 35, 59)( 36, 60)( 37, 62)( 38, 61)( 39, 57)( 40, 58)( 41, 71)( 42, 72)( 43, 67)( 44, 68)( 45, 70)( 46, 69)( 47, 65)( 48, 66)( 73, 80)( 74, 79)( 75, 76)( 81, 88)( 82, 87)( 83, 84)( 89, 96)( 90, 95)( 91, 92)( 97,128)( 98,127)( 99,124)(100,123)(101,125)(102,126)(103,122)(104,121)(105,136)(106,135)(107,132)(108,131)(109,133)(110,134)(111,130)(112,129)(113,144)(114,143)(115,140)(116,139)(117,141)(118,142)(119,138)(120,137);; 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,
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*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0,
s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(146)!( 1, 73)( 2, 74)( 3, 78)( 4, 77)( 5, 76)( 6, 75)( 7, 80)( 8, 79)( 9, 89)( 10, 90)( 11, 94)( 12, 93)( 13, 92)( 14, 91)( 15, 96)( 16, 95)( 17, 81)( 18, 82)( 19, 86)( 20, 85)( 21, 84)( 22, 83)( 23, 88)( 24, 87)( 25,121)( 26,122)( 27,126)( 28,125)( 29,124)( 30,123)( 31,128)( 32,127)( 33,137)( 34,138)( 35,142)( 36,141)( 37,140)( 38,139)( 39,144)( 40,143)( 41,129)( 42,130)( 43,134)( 44,133)( 45,132)( 46,131)( 47,136)( 48,135)( 49, 97)( 50, 98)( 51,102)( 52,101)( 53,100)( 54, 99)( 55,104)( 56,103)( 57,113)( 58,114)( 59,118)( 60,117)( 61,116)( 62,115)( 63,120)( 64,119)( 65,105)( 66,106)( 67,110)( 68,109)( 69,108)( 70,107)( 71,112)( 72,111); s1 := Sym(146)!( 1, 33)( 2, 34)( 3, 36)( 4, 35)( 5, 39)( 6, 40)( 7, 37)( 8, 38)( 9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 31)( 14, 32)( 15, 29)( 16, 30)( 17, 41)( 18, 42)( 19, 44)( 20, 43)( 21, 47)( 22, 48)( 23, 45)( 24, 46)( 49, 57)( 50, 58)( 51, 60)( 52, 59)( 53, 63)( 54, 64)( 55, 61)( 56, 62)( 67, 68)( 69, 71)( 70, 72)( 73,105)( 74,106)( 75,108)( 76,107)( 77,111)( 78,112)( 79,109)( 80,110)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,103)( 86,104)( 87,101)( 88,102)( 89,113)( 90,114)( 91,116)( 92,115)( 93,119)( 94,120)( 95,117)( 96,118)(121,129)(122,130)(123,132)(124,131)(125,135)(126,136)(127,133)(128,134)(139,140)(141,143)(142,144); s2 := Sym(146)!( 1, 7)( 2, 8)( 5, 6)( 9, 15)( 10, 16)( 13, 14)( 17, 23)( 18, 24)( 21, 22)( 25, 55)( 26, 56)( 27, 51)( 28, 52)( 29, 54)( 30, 53)( 31, 49)( 32, 50)( 33, 63)( 34, 64)( 35, 59)( 36, 60)( 37, 62)( 38, 61)( 39, 57)( 40, 58)( 41, 71)( 42, 72)( 43, 67)( 44, 68)( 45, 70)( 46, 69)( 47, 65)( 48, 66)( 73, 80)( 74, 79)( 75, 76)( 81, 88)( 82, 87)( 83, 84)( 89, 96)( 90, 95)( 91, 92)( 97,128)( 98,127)( 99,124)(100,123)(101,125)(102,126)(103,122)(104,121)(105,136)(106,135)(107,132)(108,131)(109,133)(110,134)(111,130)(112,129)(113,144)(114,143)(115,140)(116,139)(117,141)(118,142)(119,138)(120,137); 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, 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*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0, s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 >;