Overview
- Group
- SmallGroup(768,141633)
- Rank
- 4
- Schläfli Type
- {2,8,12}
- Vertices, edges, …
- 2, 16, 96, 24
- 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
32-fold
48-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)( 9,105)( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,114)( 16,115)( 17,116)( 18,111)( 19,112)( 20,113)( 21,120)( 22,121)( 23,122)( 24,117)( 25,118)( 26,119)( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)( 32,134)( 33,123)( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,144)( 40,145)( 41,146)( 42,141)( 43,142)( 44,143)( 45,138)( 46,139)( 47,140)( 48,135)( 49,136)( 50,137)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,153)( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,162)( 64,163)( 65,164)( 66,159)( 67,160)( 68,161)( 69,168)( 70,169)( 71,170)( 72,165)( 73,166)( 74,167)( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)( 81,171)( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,192)( 88,193)( 89,194)( 90,189)( 91,190)( 92,191)( 93,186)( 94,187)( 95,188)( 96,183)( 97,184)( 98,185);; s2 := ( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)( 27, 33)( 28, 35)( 29, 34)( 30, 36)( 31, 38)( 32, 37)( 39, 45)( 40, 47)( 41, 46)( 42, 48)( 43, 50)( 44, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 71)( 59, 70)( 60, 72)( 61, 74)( 62, 73)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 87)( 82, 89)( 83, 88)( 84, 90)( 85, 92)( 86, 91)( 99,123)(100,125)(101,124)(102,126)(103,128)(104,127)(105,129)(106,131)(107,130)(108,132)(109,134)(110,133)(111,135)(112,137)(113,136)(114,138)(115,140)(116,139)(117,141)(118,143)(119,142)(120,144)(121,146)(122,145)(147,186)(148,188)(149,187)(150,183)(151,185)(152,184)(153,192)(154,194)(155,193)(156,189)(157,191)(158,190)(159,174)(160,176)(161,175)(162,171)(163,173)(164,172)(165,180)(166,182)(167,181)(168,177)(169,179)(170,178);; s3 := ( 3, 52)( 4, 51)( 5, 53)( 6, 55)( 7, 54)( 8, 56)( 9, 58)( 10, 57)( 11, 59)( 12, 61)( 13, 60)( 14, 62)( 15, 64)( 16, 63)( 17, 65)( 18, 67)( 19, 66)( 20, 68)( 21, 70)( 22, 69)( 23, 71)( 24, 73)( 25, 72)( 26, 74)( 27, 79)( 28, 78)( 29, 80)( 30, 76)( 31, 75)( 32, 77)( 33, 85)( 34, 84)( 35, 86)( 36, 82)( 37, 81)( 38, 83)( 39, 91)( 40, 90)( 41, 92)( 42, 88)( 43, 87)( 44, 89)( 45, 97)( 46, 96)( 47, 98)( 48, 94)( 49, 93)( 50, 95)( 99,148)(100,147)(101,149)(102,151)(103,150)(104,152)(105,154)(106,153)(107,155)(108,157)(109,156)(110,158)(111,160)(112,159)(113,161)(114,163)(115,162)(116,164)(117,166)(118,165)(119,167)(120,169)(121,168)(122,170)(123,175)(124,174)(125,176)(126,172)(127,171)(128,173)(129,181)(130,180)(131,182)(132,178)(133,177)(134,179)(135,187)(136,186)(137,188)(138,184)(139,183)(140,185)(141,193)(142,192)(143,194)(144,190)(145,189)(146,191);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(194)!(1,2); s1 := Sym(194)!( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)( 9,105)( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,114)( 16,115)( 17,116)( 18,111)( 19,112)( 20,113)( 21,120)( 22,121)( 23,122)( 24,117)( 25,118)( 26,119)( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)( 32,134)( 33,123)( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,144)( 40,145)( 41,146)( 42,141)( 43,142)( 44,143)( 45,138)( 46,139)( 47,140)( 48,135)( 49,136)( 50,137)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,153)( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,162)( 64,163)( 65,164)( 66,159)( 67,160)( 68,161)( 69,168)( 70,169)( 71,170)( 72,165)( 73,166)( 74,167)( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)( 81,171)( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,192)( 88,193)( 89,194)( 90,189)( 91,190)( 92,191)( 93,186)( 94,187)( 95,188)( 96,183)( 97,184)( 98,185); s2 := Sym(194)!( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)( 27, 33)( 28, 35)( 29, 34)( 30, 36)( 31, 38)( 32, 37)( 39, 45)( 40, 47)( 41, 46)( 42, 48)( 43, 50)( 44, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 71)( 59, 70)( 60, 72)( 61, 74)( 62, 73)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 87)( 82, 89)( 83, 88)( 84, 90)( 85, 92)( 86, 91)( 99,123)(100,125)(101,124)(102,126)(103,128)(104,127)(105,129)(106,131)(107,130)(108,132)(109,134)(110,133)(111,135)(112,137)(113,136)(114,138)(115,140)(116,139)(117,141)(118,143)(119,142)(120,144)(121,146)(122,145)(147,186)(148,188)(149,187)(150,183)(151,185)(152,184)(153,192)(154,194)(155,193)(156,189)(157,191)(158,190)(159,174)(160,176)(161,175)(162,171)(163,173)(164,172)(165,180)(166,182)(167,181)(168,177)(169,179)(170,178); s3 := Sym(194)!( 3, 52)( 4, 51)( 5, 53)( 6, 55)( 7, 54)( 8, 56)( 9, 58)( 10, 57)( 11, 59)( 12, 61)( 13, 60)( 14, 62)( 15, 64)( 16, 63)( 17, 65)( 18, 67)( 19, 66)( 20, 68)( 21, 70)( 22, 69)( 23, 71)( 24, 73)( 25, 72)( 26, 74)( 27, 79)( 28, 78)( 29, 80)( 30, 76)( 31, 75)( 32, 77)( 33, 85)( 34, 84)( 35, 86)( 36, 82)( 37, 81)( 38, 83)( 39, 91)( 40, 90)( 41, 92)( 42, 88)( 43, 87)( 44, 89)( 45, 97)( 46, 96)( 47, 98)( 48, 94)( 49, 93)( 50, 95)( 99,148)(100,147)(101,149)(102,151)(103,150)(104,152)(105,154)(106,153)(107,155)(108,157)(109,156)(110,158)(111,160)(112,159)(113,161)(114,163)(115,162)(116,164)(117,166)(118,165)(119,167)(120,169)(121,168)(122,170)(123,175)(124,174)(125,176)(126,172)(127,171)(128,173)(129,181)(130,180)(131,182)(132,178)(133,177)(134,179)(135,187)(136,186)(137,188)(138,184)(139,183)(140,185)(141,193)(142,192)(143,194)(144,190)(145,189)(146,191); poly := sub<Sym(194)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;