Overview
- Group
- SmallGroup(1152,99261)
- Rank
- 4
- Schläfli Type
- {4,36,2}
- Vertices, edges, …
- 8, 144, 72, 2
- Order of s0s1s2s3
- 36
- 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
9-fold
12-fold
16-fold
18-fold
24-fold
36-fold
48-fold
72-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)( 45, 54)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)( 62, 71)( 63, 72)( 73, 91)( 74, 92)( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)( 81, 99)( 82,100)( 83,101)( 84,102)( 85,103)( 86,104)( 87,105)( 88,106)( 89,107)( 90,108)(109,136)(110,137)(111,138)(112,139)(113,140)(114,141)(115,142)(116,143)(117,144)(118,127)(119,128)(120,129)(121,130)(122,131)(123,132)(124,133)(125,134)(126,135);; s1 := ( 1, 73)( 2, 75)( 3, 74)( 4, 80)( 5, 79)( 6, 81)( 7, 77)( 8, 76)( 9, 78)( 10, 82)( 11, 84)( 12, 83)( 13, 89)( 14, 88)( 15, 90)( 16, 86)( 17, 85)( 18, 87)( 19, 91)( 20, 93)( 21, 92)( 22, 98)( 23, 97)( 24, 99)( 25, 95)( 26, 94)( 27, 96)( 28,100)( 29,102)( 30,101)( 31,107)( 32,106)( 33,108)( 34,104)( 35,103)( 36,105)( 37,109)( 38,111)( 39,110)( 40,116)( 41,115)( 42,117)( 43,113)( 44,112)( 45,114)( 46,118)( 47,120)( 48,119)( 49,125)( 50,124)( 51,126)( 52,122)( 53,121)( 54,123)( 55,127)( 56,129)( 57,128)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)( 64,136)( 65,138)( 66,137)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)( 72,141);; s2 := ( 1, 4)( 2, 6)( 3, 5)( 7, 8)( 10, 13)( 11, 15)( 12, 14)( 16, 17)( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 35)( 26, 34)( 27, 36)( 37, 40)( 38, 42)( 39, 41)( 43, 44)( 46, 49)( 47, 51)( 48, 50)( 52, 53)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 71)( 62, 70)( 63, 72)( 73,112)( 74,114)( 75,113)( 76,109)( 77,111)( 78,110)( 79,116)( 80,115)( 81,117)( 82,121)( 83,123)( 84,122)( 85,118)( 86,120)( 87,119)( 88,125)( 89,124)( 90,126)( 91,139)( 92,141)( 93,140)( 94,136)( 95,138)( 96,137)( 97,143)( 98,142)( 99,144)(100,130)(101,132)(102,131)(103,127)(104,129)(105,128)(106,134)(107,133)(108,135);; 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, s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(146)!( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)( 45, 54)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)( 62, 71)( 63, 72)( 73, 91)( 74, 92)( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)( 81, 99)( 82,100)( 83,101)( 84,102)( 85,103)( 86,104)( 87,105)( 88,106)( 89,107)( 90,108)(109,136)(110,137)(111,138)(112,139)(113,140)(114,141)(115,142)(116,143)(117,144)(118,127)(119,128)(120,129)(121,130)(122,131)(123,132)(124,133)(125,134)(126,135); s1 := Sym(146)!( 1, 73)( 2, 75)( 3, 74)( 4, 80)( 5, 79)( 6, 81)( 7, 77)( 8, 76)( 9, 78)( 10, 82)( 11, 84)( 12, 83)( 13, 89)( 14, 88)( 15, 90)( 16, 86)( 17, 85)( 18, 87)( 19, 91)( 20, 93)( 21, 92)( 22, 98)( 23, 97)( 24, 99)( 25, 95)( 26, 94)( 27, 96)( 28,100)( 29,102)( 30,101)( 31,107)( 32,106)( 33,108)( 34,104)( 35,103)( 36,105)( 37,109)( 38,111)( 39,110)( 40,116)( 41,115)( 42,117)( 43,113)( 44,112)( 45,114)( 46,118)( 47,120)( 48,119)( 49,125)( 50,124)( 51,126)( 52,122)( 53,121)( 54,123)( 55,127)( 56,129)( 57,128)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)( 64,136)( 65,138)( 66,137)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)( 72,141); s2 := Sym(146)!( 1, 4)( 2, 6)( 3, 5)( 7, 8)( 10, 13)( 11, 15)( 12, 14)( 16, 17)( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 35)( 26, 34)( 27, 36)( 37, 40)( 38, 42)( 39, 41)( 43, 44)( 46, 49)( 47, 51)( 48, 50)( 52, 53)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 71)( 62, 70)( 63, 72)( 73,112)( 74,114)( 75,113)( 76,109)( 77,111)( 78,110)( 79,116)( 80,115)( 81,117)( 82,121)( 83,123)( 84,122)( 85,118)( 86,120)( 87,119)( 88,125)( 89,124)( 90,126)( 91,139)( 92,141)( 93,140)( 94,136)( 95,138)( 96,137)( 97,143)( 98,142)( 99,144)(100,130)(101,132)(102,131)(103,127)(104,129)(105,128)(106,134)(107,133)(108,135); 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, s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;