Overview
- Group
- SmallGroup(1728,12713)
- Rank
- 3
- Schläfli Type
- {12,24}
- Vertices, edges, …
- 36, 432, 72
- Order of s0s1s2
- 8
- Order of s0s1s2s1
- 12
- 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)( 55, 82)( 56, 84)( 57, 83)( 58,103)( 59,105)( 60,104)( 61, 99)( 62, 98)( 63, 97)( 64,100)( 65,102)( 66,101)( 67, 94)( 68, 96)( 69, 95)( 70, 90)( 71, 89)( 72, 88)( 73, 91)( 74, 93)( 75, 92)( 76, 85)( 77, 87)( 78, 86)( 79,108)( 80,107)( 81,106)(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)(163,190)(164,192)(165,191)(166,211)(167,213)(168,212)(169,207)(170,206)(171,205)(172,208)(173,210)(174,209)(175,202)(176,204)(177,203)(178,198)(179,197)(180,196)(181,199)(182,201)(183,200)(184,193)(185,195)(186,194)(187,216)(188,215)(189,214);; s1 := ( 1, 2)( 4, 6)( 8, 9)( 10, 26)( 11, 25)( 12, 27)( 13, 21)( 14, 20)( 15, 19)( 16, 22)( 17, 24)( 18, 23)( 28, 29)( 31, 33)( 35, 36)( 37, 53)( 38, 52)( 39, 54)( 40, 48)( 41, 47)( 42, 46)( 43, 49)( 44, 51)( 45, 50)( 55, 83)( 56, 82)( 57, 84)( 58, 87)( 59, 86)( 60, 85)( 61, 88)( 62, 90)( 63, 89)( 64,107)( 65,106)( 66,108)( 67,102)( 68,101)( 69,100)( 70,103)( 71,105)( 72,104)( 73, 96)( 74, 95)( 75, 94)( 76, 97)( 77, 99)( 78, 98)( 79, 92)( 80, 91)( 81, 93)(109,164)(110,163)(111,165)(112,168)(113,167)(114,166)(115,169)(116,171)(117,170)(118,188)(119,187)(120,189)(121,183)(122,182)(123,181)(124,184)(125,186)(126,185)(127,177)(128,176)(129,175)(130,178)(131,180)(132,179)(133,173)(134,172)(135,174)(136,191)(137,190)(138,192)(139,195)(140,194)(141,193)(142,196)(143,198)(144,197)(145,215)(146,214)(147,216)(148,210)(149,209)(150,208)(151,211)(152,213)(153,212)(154,204)(155,203)(156,202)(157,205)(158,207)(159,206)(160,200)(161,199)(162,201);; s2 := ( 1,148)( 2,149)( 3,150)( 4,146)( 5,147)( 6,145)( 7,153)( 8,151)( 9,152)( 10,141)( 11,139)( 12,140)( 13,136)( 14,137)( 15,138)( 16,143)( 17,144)( 18,142)( 19,158)( 20,159)( 21,157)( 22,156)( 23,154)( 24,155)( 25,160)( 26,161)( 27,162)( 28,121)( 29,122)( 30,123)( 31,119)( 32,120)( 33,118)( 34,126)( 35,124)( 36,125)( 37,114)( 38,112)( 39,113)( 40,109)( 41,110)( 42,111)( 43,116)( 44,117)( 45,115)( 46,131)( 47,132)( 48,130)( 49,129)( 50,127)( 51,128)( 52,133)( 53,134)( 54,135)( 55,175)( 56,176)( 57,177)( 58,173)( 59,174)( 60,172)( 61,180)( 62,178)( 63,179)( 64,168)( 65,166)( 66,167)( 67,163)( 68,164)( 69,165)( 70,170)( 71,171)( 72,169)( 73,185)( 74,186)( 75,184)( 76,183)( 77,181)( 78,182)( 79,187)( 80,188)( 81,189)( 82,202)( 83,203)( 84,204)( 85,200)( 86,201)( 87,199)( 88,207)( 89,205)( 90,206)( 91,195)( 92,193)( 93,194)( 94,190)( 95,191)( 96,192)( 97,197)( 98,198)( 99,196)(100,212)(101,213)(102,211)(103,210)(104,208)(105,209)(106,214)(107,215)(108,216);; 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,
s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2 ];;
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)( 55, 82)( 56, 84)( 57, 83)( 58,103)( 59,105)( 60,104)( 61, 99)( 62, 98)( 63, 97)( 64,100)( 65,102)( 66,101)( 67, 94)( 68, 96)( 69, 95)( 70, 90)( 71, 89)( 72, 88)( 73, 91)( 74, 93)( 75, 92)( 76, 85)( 77, 87)( 78, 86)( 79,108)( 80,107)( 81,106)(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)(163,190)(164,192)(165,191)(166,211)(167,213)(168,212)(169,207)(170,206)(171,205)(172,208)(173,210)(174,209)(175,202)(176,204)(177,203)(178,198)(179,197)(180,196)(181,199)(182,201)(183,200)(184,193)(185,195)(186,194)(187,216)(188,215)(189,214); s1 := Sym(216)!( 1, 2)( 4, 6)( 8, 9)( 10, 26)( 11, 25)( 12, 27)( 13, 21)( 14, 20)( 15, 19)( 16, 22)( 17, 24)( 18, 23)( 28, 29)( 31, 33)( 35, 36)( 37, 53)( 38, 52)( 39, 54)( 40, 48)( 41, 47)( 42, 46)( 43, 49)( 44, 51)( 45, 50)( 55, 83)( 56, 82)( 57, 84)( 58, 87)( 59, 86)( 60, 85)( 61, 88)( 62, 90)( 63, 89)( 64,107)( 65,106)( 66,108)( 67,102)( 68,101)( 69,100)( 70,103)( 71,105)( 72,104)( 73, 96)( 74, 95)( 75, 94)( 76, 97)( 77, 99)( 78, 98)( 79, 92)( 80, 91)( 81, 93)(109,164)(110,163)(111,165)(112,168)(113,167)(114,166)(115,169)(116,171)(117,170)(118,188)(119,187)(120,189)(121,183)(122,182)(123,181)(124,184)(125,186)(126,185)(127,177)(128,176)(129,175)(130,178)(131,180)(132,179)(133,173)(134,172)(135,174)(136,191)(137,190)(138,192)(139,195)(140,194)(141,193)(142,196)(143,198)(144,197)(145,215)(146,214)(147,216)(148,210)(149,209)(150,208)(151,211)(152,213)(153,212)(154,204)(155,203)(156,202)(157,205)(158,207)(159,206)(160,200)(161,199)(162,201); s2 := Sym(216)!( 1,148)( 2,149)( 3,150)( 4,146)( 5,147)( 6,145)( 7,153)( 8,151)( 9,152)( 10,141)( 11,139)( 12,140)( 13,136)( 14,137)( 15,138)( 16,143)( 17,144)( 18,142)( 19,158)( 20,159)( 21,157)( 22,156)( 23,154)( 24,155)( 25,160)( 26,161)( 27,162)( 28,121)( 29,122)( 30,123)( 31,119)( 32,120)( 33,118)( 34,126)( 35,124)( 36,125)( 37,114)( 38,112)( 39,113)( 40,109)( 41,110)( 42,111)( 43,116)( 44,117)( 45,115)( 46,131)( 47,132)( 48,130)( 49,129)( 50,127)( 51,128)( 52,133)( 53,134)( 54,135)( 55,175)( 56,176)( 57,177)( 58,173)( 59,174)( 60,172)( 61,180)( 62,178)( 63,179)( 64,168)( 65,166)( 66,167)( 67,163)( 68,164)( 69,165)( 70,170)( 71,171)( 72,169)( 73,185)( 74,186)( 75,184)( 76,183)( 77,181)( 78,182)( 79,187)( 80,188)( 81,189)( 82,202)( 83,203)( 84,204)( 85,200)( 86,201)( 87,199)( 88,207)( 89,205)( 90,206)( 91,195)( 92,193)( 93,194)( 94,190)( 95,191)( 96,192)( 97,197)( 98,198)( 99,196)(100,212)(101,213)(102,211)(103,210)(104,208)(105,209)(106,214)(107,215)(108,216); 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, s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2 >;
References
None.
to this polytope.