Overview
- Group
- SmallGroup(1728,12703)
- Rank
- 3
- Schläfli Type
- {12,8}
- Vertices, edges, …
- 108, 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.
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2*s2> of order 2
36 facets
- 36 of {12}*24
54 vertex figures
- 54 of {8}*16
P/N, where N=<s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 3
24 facets
- 24 of {12}*24
36 vertex figures
- 36 of {8}*16
P/N, where N=<(s0*s1)^6, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 6
16 facets
18 vertex figures
- 18 of {8}*16
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s0*s1)^6> of order 6
16 facets
18 vertex figures
- 18 of {8}*16
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^3> of order 6
12 facets
- 12 of {12}*24
18 vertex figures
- 18 of {8}*16
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, 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 := ( 1,121)( 2,123)( 3,122)( 4,129)( 5,128)( 6,127)( 7,115)( 8,117)( 9,116)( 10,131)( 11,130)( 12,132)( 13,109)( 14,111)( 15,110)( 16,125)( 17,124)( 18,126)( 19,114)( 20,113)( 21,112)( 22,119)( 23,118)( 24,120)( 25,135)( 26,134)( 27,133)( 28,148)( 29,150)( 30,149)( 31,156)( 32,155)( 33,154)( 34,142)( 35,144)( 36,143)( 37,158)( 38,157)( 39,159)( 40,136)( 41,138)( 42,137)( 43,152)( 44,151)( 45,153)( 46,141)( 47,140)( 48,139)( 49,146)( 50,145)( 51,147)( 52,162)( 53,161)( 54,160)( 55,202)( 56,204)( 57,203)( 58,210)( 59,209)( 60,208)( 61,196)( 62,198)( 63,197)( 64,212)( 65,211)( 66,213)( 67,190)( 68,192)( 69,191)( 70,206)( 71,205)( 72,207)( 73,195)( 74,194)( 75,193)( 76,200)( 77,199)( 78,201)( 79,216)( 80,215)( 81,214)( 82,175)( 83,177)( 84,176)( 85,183)( 86,182)( 87,181)( 88,169)( 89,171)( 90,170)( 91,185)( 92,184)( 93,186)( 94,163)( 95,165)( 96,164)( 97,179)( 98,178)( 99,180)(100,168)(101,167)(102,166)(103,173)(104,172)(105,174)(106,189)(107,188)(108,187);; 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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*s2*s0*s1*s0*s1*s0*s1*s0*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, 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)!( 1,121)( 2,123)( 3,122)( 4,129)( 5,128)( 6,127)( 7,115)( 8,117)( 9,116)( 10,131)( 11,130)( 12,132)( 13,109)( 14,111)( 15,110)( 16,125)( 17,124)( 18,126)( 19,114)( 20,113)( 21,112)( 22,119)( 23,118)( 24,120)( 25,135)( 26,134)( 27,133)( 28,148)( 29,150)( 30,149)( 31,156)( 32,155)( 33,154)( 34,142)( 35,144)( 36,143)( 37,158)( 38,157)( 39,159)( 40,136)( 41,138)( 42,137)( 43,152)( 44,151)( 45,153)( 46,141)( 47,140)( 48,139)( 49,146)( 50,145)( 51,147)( 52,162)( 53,161)( 54,160)( 55,202)( 56,204)( 57,203)( 58,210)( 59,209)( 60,208)( 61,196)( 62,198)( 63,197)( 64,212)( 65,211)( 66,213)( 67,190)( 68,192)( 69,191)( 70,206)( 71,205)( 72,207)( 73,195)( 74,194)( 75,193)( 76,200)( 77,199)( 78,201)( 79,216)( 80,215)( 81,214)( 82,175)( 83,177)( 84,176)( 85,183)( 86,182)( 87,181)( 88,169)( 89,171)( 90,170)( 91,185)( 92,184)( 93,186)( 94,163)( 95,165)( 96,164)( 97,179)( 98,178)( 99,180)(100,168)(101,167)(102,166)(103,173)(104,172)(105,174)(106,189)(107,188)(108,187); 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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*s2*s0*s1*s0*s1*s0*s1*s0*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.