Overview
- Group
- SmallGroup(1728,12703)
- Rank
- 3
- Schläfli Type
- {12,24}
- Vertices, edges, …
- 36, 432, 72
- Order of s0s1s2
- 24
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
24-fold
27-fold
54-fold
108-fold
216-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 22)( 5, 24)( 6, 23)( 7, 18)( 8, 17)( 9, 16)( 10, 19)( 11, 21)( 12, 20)( 14, 15)( 25, 27)( 29, 30)( 31, 49)( 32, 51)( 33, 50)( 34, 45)( 35, 44)( 36, 43)( 37, 46)( 38, 48)( 39, 47)( 41, 42)( 52, 54)( 56, 57)( 58, 76)( 59, 78)( 60, 77)( 61, 72)( 62, 71)( 63, 70)( 64, 73)( 65, 75)( 66, 74)( 68, 69)( 79, 81)( 83, 84)( 85,103)( 86,105)( 87,104)( 88, 99)( 89, 98)( 90, 97)( 91,100)( 92,102)( 93,101)( 95, 96)(106,108)(110,111)(112,130)(113,132)(114,131)(115,126)(116,125)(117,124)(118,127)(119,129)(120,128)(122,123)(133,135)(137,138)(139,157)(140,159)(141,158)(142,153)(143,152)(144,151)(145,154)(146,156)(147,155)(149,150)(160,162)(164,165)(166,184)(167,186)(168,185)(169,180)(170,179)(171,178)(172,181)(173,183)(174,182)(176,177)(187,189)(191,192)(193,211)(194,213)(195,212)(196,207)(197,206)(198,205)(199,208)(200,210)(201,209)(203,204)(214,216);; s1 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)( 10, 13)( 11, 15)( 12, 14)( 17, 18)( 19, 25)( 20, 27)( 21, 26)( 23, 24)( 28, 29)( 31, 35)( 32, 34)( 33, 36)( 37, 40)( 38, 42)( 39, 41)( 44, 45)( 46, 52)( 47, 54)( 48, 53)( 50, 51)( 55, 83)( 56, 82)( 57, 84)( 58, 89)( 59, 88)( 60, 90)( 61, 86)( 62, 85)( 63, 87)( 64, 94)( 65, 96)( 66, 95)( 67, 91)( 68, 93)( 69, 92)( 70, 97)( 71, 99)( 72, 98)( 73,106)( 74,108)( 75,107)( 76,103)( 77,105)( 78,104)( 79,100)( 80,102)( 81,101)(109,164)(110,163)(111,165)(112,170)(113,169)(114,171)(115,167)(116,166)(117,168)(118,175)(119,177)(120,176)(121,172)(122,174)(123,173)(124,178)(125,180)(126,179)(127,187)(128,189)(129,188)(130,184)(131,186)(132,185)(133,181)(134,183)(135,182)(136,191)(137,190)(138,192)(139,197)(140,196)(141,198)(142,194)(143,193)(144,195)(145,202)(146,204)(147,203)(148,199)(149,201)(150,200)(151,205)(152,207)(153,206)(154,214)(155,216)(156,215)(157,211)(158,213)(159,212)(160,208)(161,210)(162,209);; s2 := ( 1,121)( 2,122)( 3,123)( 4,119)( 5,120)( 6,118)( 7,126)( 8,124)( 9,125)( 10,114)( 11,112)( 12,113)( 13,109)( 14,110)( 15,111)( 16,116)( 17,117)( 18,115)( 19,131)( 20,132)( 21,130)( 22,129)( 23,127)( 24,128)( 25,133)( 26,134)( 27,135)( 28,148)( 29,149)( 30,150)( 31,146)( 32,147)( 33,145)( 34,153)( 35,151)( 36,152)( 37,141)( 38,139)( 39,140)( 40,136)( 41,137)( 42,138)( 43,143)( 44,144)( 45,142)( 46,158)( 47,159)( 48,157)( 49,156)( 50,154)( 51,155)( 52,160)( 53,161)( 54,162)( 55,202)( 56,203)( 57,204)( 58,200)( 59,201)( 60,199)( 61,207)( 62,205)( 63,206)( 64,195)( 65,193)( 66,194)( 67,190)( 68,191)( 69,192)( 70,197)( 71,198)( 72,196)( 73,212)( 74,213)( 75,211)( 76,210)( 77,208)( 78,209)( 79,214)( 80,215)( 81,216)( 82,175)( 83,176)( 84,177)( 85,173)( 86,174)( 87,172)( 88,180)( 89,178)( 90,179)( 91,168)( 92,166)( 93,167)( 94,163)( 95,164)( 96,165)( 97,170)( 98,171)( 99,169)(100,185)(101,186)(102,184)(103,183)(104,181)(105,182)(106,187)(107,188)(108,189);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*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*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(216)!( 2, 3)( 4, 22)( 5, 24)( 6, 23)( 7, 18)( 8, 17)( 9, 16)( 10, 19)( 11, 21)( 12, 20)( 14, 15)( 25, 27)( 29, 30)( 31, 49)( 32, 51)( 33, 50)( 34, 45)( 35, 44)( 36, 43)( 37, 46)( 38, 48)( 39, 47)( 41, 42)( 52, 54)( 56, 57)( 58, 76)( 59, 78)( 60, 77)( 61, 72)( 62, 71)( 63, 70)( 64, 73)( 65, 75)( 66, 74)( 68, 69)( 79, 81)( 83, 84)( 85,103)( 86,105)( 87,104)( 88, 99)( 89, 98)( 90, 97)( 91,100)( 92,102)( 93,101)( 95, 96)(106,108)(110,111)(112,130)(113,132)(114,131)(115,126)(116,125)(117,124)(118,127)(119,129)(120,128)(122,123)(133,135)(137,138)(139,157)(140,159)(141,158)(142,153)(143,152)(144,151)(145,154)(146,156)(147,155)(149,150)(160,162)(164,165)(166,184)(167,186)(168,185)(169,180)(170,179)(171,178)(172,181)(173,183)(174,182)(176,177)(187,189)(191,192)(193,211)(194,213)(195,212)(196,207)(197,206)(198,205)(199,208)(200,210)(201,209)(203,204)(214,216); s1 := Sym(216)!( 1, 2)( 4, 8)( 5, 7)( 6, 9)( 10, 13)( 11, 15)( 12, 14)( 17, 18)( 19, 25)( 20, 27)( 21, 26)( 23, 24)( 28, 29)( 31, 35)( 32, 34)( 33, 36)( 37, 40)( 38, 42)( 39, 41)( 44, 45)( 46, 52)( 47, 54)( 48, 53)( 50, 51)( 55, 83)( 56, 82)( 57, 84)( 58, 89)( 59, 88)( 60, 90)( 61, 86)( 62, 85)( 63, 87)( 64, 94)( 65, 96)( 66, 95)( 67, 91)( 68, 93)( 69, 92)( 70, 97)( 71, 99)( 72, 98)( 73,106)( 74,108)( 75,107)( 76,103)( 77,105)( 78,104)( 79,100)( 80,102)( 81,101)(109,164)(110,163)(111,165)(112,170)(113,169)(114,171)(115,167)(116,166)(117,168)(118,175)(119,177)(120,176)(121,172)(122,174)(123,173)(124,178)(125,180)(126,179)(127,187)(128,189)(129,188)(130,184)(131,186)(132,185)(133,181)(134,183)(135,182)(136,191)(137,190)(138,192)(139,197)(140,196)(141,198)(142,194)(143,193)(144,195)(145,202)(146,204)(147,203)(148,199)(149,201)(150,200)(151,205)(152,207)(153,206)(154,214)(155,216)(156,215)(157,211)(158,213)(159,212)(160,208)(161,210)(162,209); s2 := Sym(216)!( 1,121)( 2,122)( 3,123)( 4,119)( 5,120)( 6,118)( 7,126)( 8,124)( 9,125)( 10,114)( 11,112)( 12,113)( 13,109)( 14,110)( 15,111)( 16,116)( 17,117)( 18,115)( 19,131)( 20,132)( 21,130)( 22,129)( 23,127)( 24,128)( 25,133)( 26,134)( 27,135)( 28,148)( 29,149)( 30,150)( 31,146)( 32,147)( 33,145)( 34,153)( 35,151)( 36,152)( 37,141)( 38,139)( 39,140)( 40,136)( 41,137)( 42,138)( 43,143)( 44,144)( 45,142)( 46,158)( 47,159)( 48,157)( 49,156)( 50,154)( 51,155)( 52,160)( 53,161)( 54,162)( 55,202)( 56,203)( 57,204)( 58,200)( 59,201)( 60,199)( 61,207)( 62,205)( 63,206)( 64,195)( 65,193)( 66,194)( 67,190)( 68,191)( 69,192)( 70,197)( 71,198)( 72,196)( 73,212)( 74,213)( 75,211)( 76,210)( 77,208)( 78,209)( 79,214)( 80,215)( 81,216)( 82,175)( 83,176)( 84,177)( 85,173)( 86,174)( 87,172)( 88,180)( 89,178)( 90,179)( 91,168)( 92,166)( 93,167)( 94,163)( 95,164)( 96,165)( 97,170)( 98,171)( 99,169)(100,185)(101,186)(102,184)(103,183)(104,181)(105,182)(106,187)(107,188)(108,189); poly := sub<Sym(216)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*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*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.