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