Overview
- Group
- SmallGroup(768,323305)
- Rank
- 4
- Schläfli Type
- {12,16,2}
- Vertices, edges, …
- 12, 96, 16, 2
- Order of s0s1s2s3
- 48
- 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, 73)( 26, 75)( 27, 74)( 28, 76)( 29, 78)( 30, 77)( 31, 79)( 32, 81)( 33, 80)( 34, 82)( 35, 84)( 36, 83)( 37, 85)( 38, 87)( 39, 86)( 40, 88)( 41, 90)( 42, 89)( 43, 91)( 44, 93)( 45, 92)( 46, 94)( 47, 96)( 48, 95)( 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)(121,169)(122,171)(123,170)(124,172)(125,174)(126,173)(127,175)(128,177)(129,176)(130,178)(131,180)(132,179)(133,181)(134,183)(135,182)(136,184)(137,186)(138,185)(139,187)(140,189)(141,188)(142,190)(143,192)(144,191);; s1 := ( 1, 2)( 4, 5)( 7, 11)( 8, 10)( 9, 12)( 13, 14)( 16, 17)( 19, 23)( 20, 22)( 21, 24)( 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, 71)( 56, 70)( 57, 72)( 58, 68)( 59, 67)( 60, 69)( 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)(103,131)(104,130)(105,132)(106,128)(107,127)(108,129)(109,134)(110,133)(111,135)(112,137)(113,136)(114,138)(115,143)(116,142)(117,144)(118,140)(119,139)(120,141)(145,182)(146,181)(147,183)(148,185)(149,184)(150,186)(151,191)(152,190)(153,192)(154,188)(155,187)(156,189)(157,170)(158,169)(159,171)(160,173)(161,172)(162,174)(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)( 7,106)( 8,107)( 9,108)( 10,103)( 11,104)( 12,105)( 13,109)( 14,110)( 15,111)( 16,112)( 17,113)( 18,114)( 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)( 37,139)( 38,140)( 39,141)( 40,142)( 41,143)( 42,144)( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 48,138)( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,154)( 56,155)( 57,156)( 58,151)( 59,152)( 60,153)( 61,157)( 62,158)( 63,159)( 64,160)( 65,161)( 66,162)( 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)( 85,187)( 86,188)( 87,189)( 88,190)( 89,191)( 90,192)( 91,181)( 92,182)( 93,183)( 94,184)( 95,185)( 96,186);; 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*s0*s1*s2*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,
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(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, 73)( 26, 75)( 27, 74)( 28, 76)( 29, 78)( 30, 77)( 31, 79)( 32, 81)( 33, 80)( 34, 82)( 35, 84)( 36, 83)( 37, 85)( 38, 87)( 39, 86)( 40, 88)( 41, 90)( 42, 89)( 43, 91)( 44, 93)( 45, 92)( 46, 94)( 47, 96)( 48, 95)( 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)(121,169)(122,171)(123,170)(124,172)(125,174)(126,173)(127,175)(128,177)(129,176)(130,178)(131,180)(132,179)(133,181)(134,183)(135,182)(136,184)(137,186)(138,185)(139,187)(140,189)(141,188)(142,190)(143,192)(144,191); s1 := Sym(194)!( 1, 2)( 4, 5)( 7, 11)( 8, 10)( 9, 12)( 13, 14)( 16, 17)( 19, 23)( 20, 22)( 21, 24)( 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, 71)( 56, 70)( 57, 72)( 58, 68)( 59, 67)( 60, 69)( 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)(103,131)(104,130)(105,132)(106,128)(107,127)(108,129)(109,134)(110,133)(111,135)(112,137)(113,136)(114,138)(115,143)(116,142)(117,144)(118,140)(119,139)(120,141)(145,182)(146,181)(147,183)(148,185)(149,184)(150,186)(151,191)(152,190)(153,192)(154,188)(155,187)(156,189)(157,170)(158,169)(159,171)(160,173)(161,172)(162,174)(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)( 7,106)( 8,107)( 9,108)( 10,103)( 11,104)( 12,105)( 13,109)( 14,110)( 15,111)( 16,112)( 17,113)( 18,114)( 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)( 37,139)( 38,140)( 39,141)( 40,142)( 41,143)( 42,144)( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 48,138)( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,154)( 56,155)( 57,156)( 58,151)( 59,152)( 60,153)( 61,157)( 62,158)( 63,159)( 64,160)( 65,161)( 66,162)( 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)( 85,187)( 86,188)( 87,189)( 88,190)( 89,191)( 90,192)( 91,181)( 92,182)( 93,183)( 94,184)( 95,185)( 96,186); 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*s0*s1*s2*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, 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 >;