Overview
- Group
- SmallGroup(1248,1329)
- Rank
- 4
- Schläfli Type
- {26,4,6}
- Vertices, edges, …
- 26, 52, 12, 6
- Order of s0s1s2s3
- 156
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{26,4|2},{4,6|2}}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
13-fold
26-fold
39-fold
52-fold
78-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 := ( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)( 31, 36)( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 80, 91)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)( 98, 99)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(132,143)(133,142)(134,141)(135,140)(136,139)(137,138)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151);; s1 := ( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 15)( 16, 26)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 28)( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 46, 48)( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 66, 67)( 68, 78)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79,119)( 80,118)( 81,130)( 82,129)( 83,128)( 84,127)( 85,126)( 86,125)( 87,124)( 88,123)( 89,122)( 90,121)( 91,120)( 92,132)( 93,131)( 94,143)( 95,142)( 96,141)( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)(104,133)(105,145)(106,144)(107,156)(108,155)(109,154)(110,153)(111,152)(112,151)(113,150)(114,149)(115,148)(116,147)(117,146);; s2 := ( 1, 79)( 2, 80)( 3, 81)( 4, 82)( 5, 83)( 6, 84)( 7, 85)( 8, 86)( 9, 87)( 10, 88)( 11, 89)( 12, 90)( 13, 91)( 14,105)( 15,106)( 16,107)( 17,108)( 18,109)( 19,110)( 20,111)( 21,112)( 22,113)( 23,114)( 24,115)( 25,116)( 26,117)( 27, 92)( 28, 93)( 29, 94)( 30, 95)( 31, 96)( 32, 97)( 33, 98)( 34, 99)( 35,100)( 36,101)( 37,102)( 38,103)( 39,104)( 40,118)( 41,119)( 42,120)( 43,121)( 44,122)( 45,123)( 46,124)( 47,125)( 48,126)( 49,127)( 50,128)( 51,129)( 52,130)( 53,144)( 54,145)( 55,146)( 56,147)( 57,148)( 58,149)( 59,150)( 60,151)( 61,152)( 62,153)( 63,154)( 64,155)( 65,156)( 66,131)( 67,132)( 68,133)( 69,134)( 70,135)( 71,136)( 72,137)( 73,138)( 74,139)( 75,140)( 76,141)( 77,142)( 78,143);; s3 := ( 1, 14)( 2, 15)( 3, 16)( 4, 17)( 5, 18)( 6, 19)( 7, 20)( 8, 21)( 9, 22)( 10, 23)( 11, 24)( 12, 25)( 13, 26)( 40, 53)( 41, 54)( 42, 55)( 43, 56)( 44, 57)( 45, 58)( 46, 59)( 47, 60)( 48, 61)( 49, 62)( 50, 63)( 51, 64)( 52, 65)( 79, 92)( 80, 93)( 81, 94)( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)( 90,103)( 91,104)(118,131)(119,132)(120,133)(121,134)(122,135)(123,136)(124,137)(125,138)(126,139)(127,140)(128,141)(129,142)(130,143);; 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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(156)!( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)( 31, 36)( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 80, 91)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)( 98, 99)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(132,143)(133,142)(134,141)(135,140)(136,139)(137,138)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151); s1 := Sym(156)!( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 15)( 16, 26)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 28)( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 46, 48)( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 66, 67)( 68, 78)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79,119)( 80,118)( 81,130)( 82,129)( 83,128)( 84,127)( 85,126)( 86,125)( 87,124)( 88,123)( 89,122)( 90,121)( 91,120)( 92,132)( 93,131)( 94,143)( 95,142)( 96,141)( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)(104,133)(105,145)(106,144)(107,156)(108,155)(109,154)(110,153)(111,152)(112,151)(113,150)(114,149)(115,148)(116,147)(117,146); s2 := Sym(156)!( 1, 79)( 2, 80)( 3, 81)( 4, 82)( 5, 83)( 6, 84)( 7, 85)( 8, 86)( 9, 87)( 10, 88)( 11, 89)( 12, 90)( 13, 91)( 14,105)( 15,106)( 16,107)( 17,108)( 18,109)( 19,110)( 20,111)( 21,112)( 22,113)( 23,114)( 24,115)( 25,116)( 26,117)( 27, 92)( 28, 93)( 29, 94)( 30, 95)( 31, 96)( 32, 97)( 33, 98)( 34, 99)( 35,100)( 36,101)( 37,102)( 38,103)( 39,104)( 40,118)( 41,119)( 42,120)( 43,121)( 44,122)( 45,123)( 46,124)( 47,125)( 48,126)( 49,127)( 50,128)( 51,129)( 52,130)( 53,144)( 54,145)( 55,146)( 56,147)( 57,148)( 58,149)( 59,150)( 60,151)( 61,152)( 62,153)( 63,154)( 64,155)( 65,156)( 66,131)( 67,132)( 68,133)( 69,134)( 70,135)( 71,136)( 72,137)( 73,138)( 74,139)( 75,140)( 76,141)( 77,142)( 78,143); s3 := Sym(156)!( 1, 14)( 2, 15)( 3, 16)( 4, 17)( 5, 18)( 6, 19)( 7, 20)( 8, 21)( 9, 22)( 10, 23)( 11, 24)( 12, 25)( 13, 26)( 40, 53)( 41, 54)( 42, 55)( 43, 56)( 44, 57)( 45, 58)( 46, 59)( 47, 60)( 48, 61)( 49, 62)( 50, 63)( 51, 64)( 52, 65)( 79, 92)( 80, 93)( 81, 94)( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)( 90,103)( 91,104)(118,131)(119,132)(120,133)(121,134)(122,135)(123,136)(124,137)(125,138)(126,139)(127,140)(128,141)(129,142)(130,143); poly := sub<Sym(156)|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, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.