Template:Polyhedra DB

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{{{{{1}}}|{{{2}}}|

|key-name=Name| |key-image=PNG Image| |key-image2=JPEG Image| |key-image3=GIF Image| |key-Wythoff=Wythoff symbol| |key-W=Wenninger number| |key-U=Uniform number| |key-K=Kalido number| |key-C=Coxeter number| |key-V=Number of vertices| |key-E=Number of edges| |key-F=Number of faces |key-Fdetail=Face configuration| |key-chi=Euler characteristic| |key-vfig=Vertex figure| |key-vfigimage=Vertex figure image| |key-group=Symmetry group| |key-B=Bowers pet name| |key-altname1=alternative name| |key-altname2=second alternative name| |key-dual=Dual polyhedron name |key-special=special properties |key-schl=Schlafli symbol

|key2-name=Name| |key2-image=| |key2-image2=| |key2-Wythoff=Wythoff| |key2-W=#| |key2-U=#| |key2-K=#| |key2-C=#| |key2-V=V| |key2-E=E| |key2-F=F| |key2-Fdetail=F-types| |key2-chi=χ| |key2-vfig=Vertex figure| |key2-vfigimage=| |key2-group=Sym| |key2-B=Bowers| |key2-altname1=name2| |key2-altname2=name3| |key2-dual=dual name| |key2-special=special properties |key2-schl={p,q} |key2-dihedral=Diahedral angle


|T-name=Tetrahedron|T-image=tetrahedron.png|T-image2=tetrahedron.jpg| T-Wythoff=3 | 3 2| |T-W=1|T-U=01|T-K=06|T-C=15|T-V=4|T-E=6|T-F=4|T-Fdetail=4{3}|T-chi=2| |T-vfig=3.3.3|T-vfigimage=tetrahedron_vertfig.png|T-group=Td| |T-B=Tet|T-dual=Tetrahedron|T-dihedral=70.528779° = arccos(1/3) |T-special=deltahedron|T-schl={3,3}

|O-name=Octahedron|O-image=octahedron.png|O-image2=octahedron.jpg| O-Wythoff=4 | 3 2| |O-W=2|O-U=05|O-K=10|O-C=17|O-V=6|O-E=12|O-F=8|O-Fdetail=8{3}|O-chi=2| |O-vfig=3.3.3.3|O-vfigimage=octahedron_vertfig.png|O-group=Oh| |O-B=Oct|O-dual=Cube|O-dihedral=109.47122° = arccos(-1/3) |O-special=deltahedron|O-schl={3,4}

|C-name=Hexahedron|C-image=hexahedron.png|C-image2=hexahedron.jpg| C-altname=(Hexahedron)
|C-Wythoff=3 | 4 2| |C-W=3|C-U=06|C-K=11|C-C=18|C-V=8|C-E=12|C-F=6|C-Fdetail=6{4}|C-chi=2|C-group=Oh| |C-vfig=4.4.4|C-vfigimage=Cube_vertfig.png| |C-B=Cube|C-dual=Octahedron|C-dihedral=90° |C-special=zonohedron|C-schl={4,3}

|D-name=Dodecahedron|D-image=dodecahedron.png|D-image2=dodecahedron.jpg |D-Wythoff=3 | 5 2| |D-W=5|D-U=23|D-K=28|D-C=26|D-V=20|D-E=30|D-F=12|D-Fdetail=12{5}|D-chi=2| |D-vfig=5.5.5|D-vfigimage=dodecahedron_vertfig.png|D-group=Ih| |D-B=Doe|D-dual=Icosahedron|D-dihedral=116.56505° = arccos(-√5/5) |D-special=|D-schl={5,3}

|I-name=Icosahedron|I-image=icosahedron.png|I-image2=icosahedron.jpg| I-Wythoff=5 | 3 2| |I-W=4|I-U=22|I-K=27|I-C=25|I-V=12|I-E=30|I-F=20|I-Fdetail=20{3}|I-chi=2| |I-vfig=3.3.3.3.3|I-vfigimage=icosahedron_vertfig.png|I-group=Ih| |I-B=Ike|I-dual=Dodecahedron|I-dihedral=138.189685° = arccos(-√5/3) |I-special=deltahedron|I-schl={3,5}

|gI-name=Great icosahedron|gI-image=Great icosahedron.png| |gI-Wythoff=5/2 | 2 3| |gI-altname=(16th stellation of icosahedron)| |gI-W=41|gI-U=53|gI-K=58|gI-C=69| |gI-V=12|gI-E=30|gI-F=20|gI-Fdetail=20{3}| |gI-chi=2|gI-group=Ih| |gI-vfig=3.3.3.3.3|gI-vfigimage=Great icosahedron_vertfig.png| |gI-B=Gike|

|gD-name=Great dodecahedron| |gD-image=Great dodecahedron.png| |gD-vfigimage=Great dodecahedron_vertfig.png|gD-vfig=5.5.5.5.5| |gD-Wythoff=5/2 | 2 5| |gD-W=21|gD-U=35|gD-K=40|gD-C=44| |gD-V=12|gD-E=30|gD-F=12|gD-Fdetail=12{5}| |gD-chi=-6|gD-group=Ih| |gD-B=Gad|

|lsD-name=Small stellated dodecahedron| |lsD-image=Small stellated dodecahedron.png| |lsD-vfigimage=Small stellated dodecahedron_vertfig.png|lsD-vfig=5/2.5/2.5/2.5/2.5/2| |lsD-Wythoff=5 | 25/2| |lsD-W=20|lsD-U=34|lsD-K=39|lsD-C=43| |lsD-V=12|lsD-E=30|lsD-F=12|lsD-Fdetail=12{5/2}| |lsD-chi=-6|lsD-group=Ih| |lsD-B=Sissid|

|gsD-name=Great stellated dodecahedron| |gsD-image=Great stellated dodecahedron.png| |gsD-vfigimage=Great stellated dodecahedron_vertfig.png|gsD-vfig=5/2.5/2.5/2| |gsD-Wythoff=3 | 25/2| |gsD-W=22|gsD-U=52|gsD-K=57|gsD-C=68| |gsD-V=20|gsD-E=30|gsD-F=12|gsD-Fdetail=12{5/2}| |gsD-chi=2|gsD-group=Ih| |gsD-B=Gissid|

|CO-name=Cuboctahedron| |CO-image=Cuboctahedron.png| |CO-vfigimage=Cuboctahedron_vertfig.png|CO-vfig=3.4.3.4| |CO-Wythoff=2 | 3 4| |CO-W=11|CO-U=07|CO-K=12|CO-C=19| |CO-V=12|CO-E=24|CO-F=14|CO-Fdetail=8{3}+6{4}| |CO-chi=2|CO-group=Oh| |CO-B=Co|

|ID-name=Icosidodecahedron| |ID-image=Icosidodecahedron.png| |ID-vfigimage=Icosidodecahedron_vertfig.png|ID-vfig=3.5.3.5| |ID-Wythoff=2 | 3 5| |ID-W=12|ID-U=24|ID-K=29|ID-C=28| |ID-V=30|ID-E=60|ID-F=32|ID-Fdetail=20{3}+12{5}| |ID-chi=2|ID-group=Ih| |ID-B=Id|

|lrCO-name=Small rhombicuboctahedron|lrCO-image=Small rhombicuboctahedron.png| |lrCO-altname1=Rhombicuboctahedron| |lrCO-Wythoff=3 4 | 2| |lrCO-W=13|lrCO-U=10|lrCO-K=15|lrCO-C=22| |lrCO-V=24|lrCO-E=48|lrCO-F=26|lrCO-Fdetail=8{3}+(6+12){4}|lrCO-chi=2| |lrCO-vfig=3.4.4.4|lrCO-vfigimage=Small rhombicuboctahedron vertfig.png|lrCO-group=Oh| |lrCO-B=Sirco|

|lrID-name=Small rhombicosidodecahedron|lrID-image=Small rhombicosidodecahedron.png| |lrID-altname1=Rhombicosidodecahedron| |lrID-Wythoff=3 5 | 2| |lrID-W=14|lrID-U=27|lrID-K=32|lrID-C=30| |lrID-V=60|lrID-E=120|lrID-F=62|lrID-Fdetail=20{3}+30{4}+12{5}|lrID-chi=2| |lrID-vfig=3.4.5.4|lrID-vfigimage=icosahedron_vertfig.png|lrID-group=Ih| |lrID-B=Srid|

|gID-name=Great icosidodecahedron| |gID-image=Great icosidodecahedron.png| |gID-vfigimage=Great icosidodecahedron_vertfig.png|gID-vfig=3.5/2.3.5/2| |gID-Wythoff=2 | 3 5/2| |gID-W=94|gID-U=54|gID-K=59|gID-C=70| |gID-V=30|gID-E=60|gID-F=32|gID-Fdetail=20{3}+12{5/2}| |gID-chi=2|gID-group=Ih| |gID-B=Gid|

|DD-name=Dodecadodecahedron| |DD-image=Dodecadodecahedron.png| |DD-vfigimage=Dodecadodecahedron_vertfig.png|DD-vfig=5.5/2.5.5/2| |DD-Wythoff=2 | 5 5/2| |DD-W=73|DD-U=36|DD-K=41|DD-C=45| |DD-V=30|DD-E=60|DD-F=24|DD-Fdetail=12{5}+12{5/2}| |DD-chi=-6|DD-group=Ih| |DD-B=Did|

|ldID-name=Small ditrigonal icosidodecahedron| |ldID-image=Small ditrigonal icosidodecahedron.png| |ldID-vfigimage=Small ditrigonal icosidodecahedron_vertfig.png|ldID-vfig=3.5/2.3.5/2.3.5/2| |ldID-Wythoff=3 | 5/23| |ldID-W=70|ldID-U=30|ldID-K=35|ldID-C=39| |ldID-V=20|ldID-E=60|ldID-F=32|ldID-Fdetail=20{3}+12{5/2}| |ldID-chi=-8|ldID-group=Ih| |ldID-B=Sidtid|

|dDD-name=Ditrigonal dodecadodecahedron| |dDD-image=Ditrigonal dodecadodecahedron.png| |dDD-vfigimage=Ditrigonal dodecadodecahedron_vertfig.png|dDD-vfig=5.5/2.5.5/2.5.5/2| |dDD-Wythoff=3 | 5/35| |dDD-W=80|dDD-U=41|dDD-K=46|dDD-C=53| |dDD-V=20|dDD-E=60|dDD-F=24|dDD-Fdetail=12{5}+12{5/2}| |dDD-chi=-16|dDD-group=Ih| |dDD-B=Ditdid|

|gdID-name=Great ditrigonal icosidodecahedron| |gdID-image=Great ditrigonal icosidodecahedron.png| |gdID-vfigimage=Great ditrigonal icosidodecahedron_vertfig.png|gdID-vfig=3.5.3.5.3.5| |gdID-Wythoff=3/2 | 3 5| |gdID-W=87|gdID-U=47|gdID-K=52|gdID-C=61| |gdID-V=20|gdID-E=60|gdID-F=32|gdID-Fdetail=20{3}+12{5}| |gdID-chi=-8|gdID-group=Ih| |gdID-B=Gidtid|

|tT-name=Truncated tetrahedron| |tT-image=Truncated tetrahedron.png| |tT-vfigimage=Truncated tetrahedron vertfig.png|tT-vfig=3.6.6| |tT-Wythoff=2 3 | 3| |tT-W=6|tT-U=02|tT-K=07|tT-C=16| |tT-V=12|tT-E=18|tT-F=8|tT-Fdetail=4{3}+4{6}| |tT-chi=2|tT-group=Td| |tT-B=Tut|

|tO-name=Truncated octahedron| |tO-image=Truncated octahedron.png| |tO-vfigimage=Truncated octahedron vertfig.png|tO-vfig=4.8.8| |tO-Wythoff=2 4 | 3| |tO-W=7|tO-U=08|tO-K=13|tO-C=20| |tO-V=24|tO-E=36|tO-F=14|tO-Fdetail=6{4}+8{6}| |tO-chi=2|tO-group=Oh| |tO-B=Toe|

|tC-name=Truncated cube| |tC-altname1=Truncated hexahedron| |tC-image=Truncated hexahedron.png| |tC-vfigimage=Truncated cube vertfig.png|tC-vfig=3.8.8| |tC-Wythoff=2 3 | 4| |tC-W=8|tC-U=09|tC-K=14|tC-C=21| |tC-V=24|tC-E=36|tC-F=14|tC-Fdetail=8{3}+6{8}| |tC-chi=2|tC-group=Oh| |tC-B=Tic|

|tI-name=Truncated icosahedron| |tI-image=Truncated icosahedron.png| |tI-vfigimage=Truncated icosahedron vertfig.png|tI-vfig=5.6.6| |tI-Wythoff=2 5 | 3| |tI-W=9|tI-U=25|tI-K=30|tI-C=27| |tI-V=60|tI-E=90|tI-F=32|tI-Fdetail=12{5}+20{6}| |tI-chi=2|tI-group=Ih| |tI-B=Ti|

|tD-name=Truncated dodecahedron| |tD-image=Truncated dodecahedron.png| |tD-vfigimage=Truncated dodecahedron vertfig.png|tD-vfig=3.10.10| |tD-Wythoff=2 3 | 5| |tD-W=10|tD-U=26|tD-K=31|tD-C=29| |tD-V=60|tD-E=90|tD-F=32|tD-Fdetail=20{3}+12{10}| |tD-chi=2|tD-group=Ih| |tD-B=Tid|

|tgD-name=Truncated great dodecahedron| |tgD-image=Great truncated dodecahedron.png| |tgD-vfigimage=Truncated great dodecahedron_vertfig.png|tgD-vfig=5/2.10.10| |tgD-Wythoff=25/2 | 5| |tgD-W=75|tgD-U=37|tgD-K=42|tgD-C=47| |tgD-V=60|tgD-E=90|tgD-F=24|tgD-Fdetail=12{5/2}+12{10}| |tgD-chi=-6|tgD-group=Ih| |tgD-B=Tigid|

|gtI-name=Truncated great icosahedron| |gtI-image=Great truncated icosahedron.png| |gtI-vfigimage=Great truncated icosahedron_vertfig.png|gtI-vfig=5/2.6.6| |gtI-Wythoff=25/2 | 3| |gtI-W=95|gtI-U=55|gtI-K=60|gtI-C=71| |gtI-V=60|gtI-E=90|gtI-F=32|gtI-Fdetail=12{5/2}+20{6}| |gtI-chi=2|gtI-group=Ih| |gtI-B=Tiggy|

|stH-name=Stellated truncated hexahedron| |stH-image=Stellated truncated hexahedron.png| |stH-vfigimage=Stellated truncated hexahedron_vertfig.png|stH-vfig=3.8/3.8/3| |stH-altname1=Quasitruncated hexahedron| |stH-altname2=stellatruncated cube| |stH-Wythoff=2 3 | 4/3| |stH-W=92|stH-U=19|stH-K=24|stH-C=66| |stH-V=24|stH-E=36|stH-F=14|stH-Fdetail=8{3}+6{8/3}| |stH-chi=2|stH-group=Oh| |stH-B=Quith|

|lstD-name=Small stellated truncated dodecahedron| |lstD-image=Small stellated truncated dodecahedron.png| |lstD-vfigimage=Small stellated truncated dodecahedron_vertfig.png|lstD-vfig=5.10/3.10/3| |lstD-altname1=Quasitruncated small stellated dodecahedron| |lstD-altname2=Small stellatruncated dodecahedron| |lstD-Wythoff=2 5 | 5/3| |lstD-W=97|lstD-U=58|lstD-K=63|lstD-C=74| |lstD-V=60|lstD-E=90|lstD-F=24|lstD-Fdetail=12{5}+12{10/3}| |lstD-chi=-6|lstD-group=Ih| |lstD-B=Quitsissid|

|gstD-name=Great stellated truncated dodecahedron| |gstD-image=Great stellated truncated dodecahedron.png| |gstD-vfigimage=Great stellated truncated dodecahedron_vertfig.png|gstD-vfig=3.10/3.10/3| |gstD-altname1=Quasitruncated great stellated dodecahedron| |gstD-altname2=Great stellatruncated dodecahedron| |gstD-Wythoff=2 3 | 5/3| |gstD-W=104|gstD-U=66|gstD-K=71|gstD-C=83| |gstD-V=60|gstD-E=90|gstD-F=32|gstD-Fdetail=20{3}+12{10/3}| |gstD-chi=2|gstD-group=Ih| |gstD-B=Quitgissid|

|ThH-name=Tetrahemihexahedron| |ThH-image=Tetrahemihexahedron.png| |ThH-vfigimage=Tetrahemihexahedron_vertfig.png| |ThH-vfig=3.4.3/2.4| |ThH-Wythoff=3/23 | 2| |ThH-W=67|ThH-U=04|ThH-K=09|ThH-C=36| |ThH-V=6|ThH-E=12|ThH-F=7|ThH-Fdetail=4{3}+3{4}| |ThH-chi=1|ThH-group=Td| |ThH-B=Thah|

|OhO-name=Octahemioctahedron| |OhO-image=Octahemioctahedron.png| |OhO-vfigimage=Octahemioctahedron_vertfig.png|OhO-vfig=3.6.3.6| |OhO-Wythoff=3/23 | 3| |OhO-W=68|OhO-U=03|OhO-K=08|OhO-C=37| |OhO-V=12|OhO-E=24|OhO-F=12|OhO-Fdetail=8{3}+4{6}| |OhO-chi=0|OhO-group=Oh| |OhO-B=Oho|

|ChO-name=Cubohemioctahedron| |ChO-image=Cubohemioctahedron.png| |ChO-vfigimage=Cubohemioctahedron_vertfig.png|ChO-vfig=4.6.4.6| |ChO-Wythoff=4/34 | 3| |ChO-W=78|ChO-U=15|ChO-K=20|ChO-C=51| |ChO-V=12|ChO-E=24|ChO-F=10|ChO-Fdetail=6{4}+4{6}| |ChO-chi=-2|ChO-group=Oh| |ChO-B=Cho|

|lIhD-name=Small icosihemidodecahedron| |lIhD-image=Small icosihemidodecahedron.png| |lIhD-vfigimage=Small icosihemidodecahedron_vertfig.png|lIhD-vfig=3.10.3.10| |lIhD-Wythoff=3/23 | 5| |lIhD-W=89|lIhD-U=49|lIhD-K=54|lIhD-C=63| |lIhD-V=30|lIhD-E=60|lIhD-F=26|lIhD-Fdetail=20{3}+6{10}| |lIhD-chi=-4|lIhD-group=Ih| |lIhD-B=Seihid|

|lDhD-name=Small dodecahemidodecahedron| |lDhD-image=Small dodecahemidodecahedron.png| |lDhD-vfigimage=Small dodecahemidodecahedron_vertfig.png|lDhD-vfig=5.10.5.10| |lDhD-Wythoff=5/45 | 5| |lDhD-W=91|lDhD-U=51|lDhD-K=56|lDhD-C=65| |lDhD-V=30|lDhD-E=60|lDhD-F=18|lDhD-Fdetail=12{5}+6{10}| |lDhD-chi=-12|lDhD-group=Ih| |lDhD-B=Sidhid|

|gIhD-name=Great icosihemidodecahedron| |gIhD-image=Great icosihemidodecahedron.png| |gIhD-vfigimage=Great icosihemidodecahedron_vertfig.png|gIhD-vfig=3.10/3.3.10/3| |gIhD-Wythoff=3 3 | 5/3| |gIhD-W=106|gIhD-U=71|gIhD-K=76|gIhD-C=85| |gIhD-V=30|gIhD-E=60|gIhD-F=26|gIhD-Fdetail=20{3}+6{10/3}| |gIhD-chi=-4|gIhD-group=Ih| |gIhD-B=Geihid|

|gDhD-name=Great dodecahemidodecahedron| |gDhD-image=Great dodecahemidodecahedron.png| |gDhD-vfigimage=Great dodecahemidodecahedron_vertfig.png|gDhD-vfig=5/2.10/3.5/2.10/3| |gDhD-Wythoff=5/35/2 | 5/3| |gDhD-W=107|gDhD-U=70|gDhD-K=75|gDhD-C=86| |gDhD-V=30|gDhD-E=60|gDhD-F=18|gDhD-Fdetail=12{5/2}+6{10/3}| |gDhD-chi=-12|gDhD-group=Ih| |gDhD-B=Gidhid|

|gDhI-name=Great dodecahemicosahedron| |gDhI-image=Great dodecahemicosahedron.png| |gDhI-vfigimage=Great dodecahemicosahedron_vertfig.png|gDhI-vfig=5.6.5.6| |gDhI-Wythoff=5/45 | 3| |gDhI-W=102|gDhI-U=65|gDhI-K=70|gDhI-C=81| |gDhI-V=30|gDhI-E=60|gDhI-F=22|gDhI-Fdetail=12{5}+10{6}| |gDhI-chi=-8|gDhI-group=Ih| |gDhI-B=Gidhei|

|lDhI-name=Small dodecahemicosahedron| |lDhI-image=Small dodecahemicosahedron.png| |lDhI-vfigimage=Small dodecahemicosahedron_vertfig.png|lDhI-vfig=6.5/2.6.5/2| |lDhI-Wythoff=5/35/2 | 3| |lDhI-W=100|lDhI-U=62|lDhI-K=67|lDhI-C=78| |lDhI-V=30|lDhI-E=60|lDhI-F=22|lDhI-Fdetail=12{5/2}+10{6}| |lDhI-chi=-8|lDhI-group=Ih| |lDhI-B=Sidhei|

|lCCO-name=Small cubicuboctahedron| |lCCO-image=Small cubicuboctahedron.png| |lCCO-vfigimage=Small cubicuboctahedron_vertfig.png|lCCO-vfig=3.8.4.8| |lCCO-Wythoff=3/24 | 4| |lCCO-W=69|lCCO-U=13|lCCO-K=18|lCCO-C=38| |lCCO-V=24|lCCO-E=48|lCCO-F=20|lCCO-Fdetail=8{3}+6{4}+6{8}| |lCCO-chi=-4|lCCO-group=Oh| |lCCO-B=Socco|

|ugrCO-name=Uniform great rhombicuboctahedron| |ugrCO-image=Uniform great rhombicuboctahedron.png| |ugrCO-vfigimage=Great rhombicuboctahedron_vertfig.png|ugrCO-vfig=3.4.4.4| |ugrCO-altname1=Quasirhombicuboctahedron| |ugrCO-Wythoff=3/24 | 2| |ugrCO-W=85|ugrCO-U=17|ugrCO-K=22|ugrCO-C=59| |ugrCO-V=24|ugrCO-E=48|ugrCO-F=26|ugrCO-Fdetail=8{3}+(6+12){4}| |ugrCO-chi=2|ugrCO-group=Oh| |ugrCO-B=Querco|

|lDID-name=Small dodecicosidodecahedron| |lDID-image=Small dodecicosidodecahedron.png| |lDID-vfigimage=Small dodecicosidodecahedron_vertfig.png|lDID-vfig=3.10.5.10| |lDID-Wythoff=3/25 | 5| |lDID-W=72|lDID-U=33|lDID-K=38|lDID-C=42| |lDID-V=60|lDID-E=120|lDID-F=44|lDID-Fdetail=20{3}+12{5}+12{10}| |lDID-chi=-16|lDID-group=Ih| |lDID-B=Saddid|

|gIID-name=Great icosicosidodecahedron| |gIID-image=Great icosicosidodecahedron.png| |gIID-vfigimage=Great icosicosidodecahedron_vertfig.png|gIID-vfig=3.6.5.6| |gIID-Wythoff=3/25 | 3| |gIID-W=88|gIID-U=48|gIID-K=53|gIID-C=62| |gIID-V=60|gIID-E=120|gIID-F=52|gIID-Fdetail=20{3}+12{5}+20{6}| |gIID-chi=-8|gIID-group=Ih| |gIID-B=Giid|

|ldDID-name=Small ditrigonal dodecicosidodecahedron| |ldDID-image=Small ditrigonal dodecicosidodecahedron.png| |ldDID-vfigimage=Small ditrigonal dodecicosidodecahedron_vertfig.png|ldDID-vfig=3.10.5/2.10| |ldDID-Wythoff=5/33 | 5| |ldDID-W=82|ldDID-U=43|ldDID-K=48|ldDID-C=55| |ldDID-V=60|ldDID-E=120|ldDID-F=44|ldDID-Fdetail=20{3}+12{5/2}+12{10}| |ldDID-chi=-16|ldDID-group=Ih| |ldDID-B=Sidditdid|

|IDD-name=Icosidodecadodecahedron| |IDD-image=Icosidodecadodecahedron.png| |IDD-vfigimage=Icosidodecadodecahedron_vertfig.png|IDD-vfig=5.6.5/2.6| |IDD-Wythoff=5/35 | 3| |IDD-W=83|IDD-U=44|IDD-K=49|IDD-C=56| |IDD-V=60|IDD-E=120|IDD-F=44|IDD-Fdetail=12{5}+12{5/2}+20{6}| |IDD-chi=-16|IDD-group=Ih| |IDD-B=Ided|

|ugrID-name=Uniform great rhombicosidodecahedron| |ugrID-image=Uniform great rhombicosidodecahedron.png| |ugrID-vfigimage=Uniform great rhombicosidodecahedron_vertfig.png|ugrID-vfig=3.4.5/2.4| |ugrID-altname1=Quasirhombicosidodecahedron| |ugrID-Wythoff=5/33 | 2| |ugrID-W=105|ugrID-U=67|ugrID-K=72|ugrID-C=84| |ugrID-V=60|ugrID-E=120|ugrID-F=62|ugrID-Fdetail=20{3}+30{4}+12{5/2}| |ugrID-chi=2|ugrID-group=Ih| |ugrID-B=Qrid|

|grCO-name=Great rhombicuboctahedron| |grCO-image=Great rhombicuboctahedron.png| |grCO-vfigimage=Great rhombicuboctahedron vertfig.png|grCO-vfig=4.6.8| |grCO-altname1=Rhombitruncated cuboctahedron| |grCO-altname2=Truncated cuboctahedron| |grCO-Wythoff=2 3 4 | | |grCO-W=15|grCO-U=11|grCO-K=16|grCO-C=23| |grCO-V=48|grCO-E=72|grCO-F=26|grCO-Fdetail=12{4}+8{6}+6{8}| |grCO-chi=2|grCO-group=Oh| |grCO-B=Girco|

|gtCO-name=Great truncated cuboctahedron| |gtCO-image=Great truncated cuboctahedron.png| |gtCO-vfigimage=Great truncated cuboctahedron_vertfig.png|gtCO-vfig=4.6.8/3| |gtCO-altname1=Quasitruncated cuboctahedron| |gtCO-Wythoff=2 34/3 | | |gtCO-W=93|gtCO-U=20|gtCO-K=25|gtCO-C=67| |gtCO-V=48|gtCO-E=72|gtCO-F=26|gtCO-Fdetail=12{4}+8{6}+6{8/3}| |gtCO-chi=2|gtCO-group=Oh| |gtCO-B=Quitco|

|lrH-name=Small rhombihexahedron| |lrH-image=Small rhombihexahedron.png| |lrH-vfigimage=Small rhombihexahedron_vertfig.png|lrH-vfig=4.8.4.8| |lrH-Wythoff=2 3/2 4 |
or 2 4 4/3| |lrH-W=86|lrH-U=18|lrH-K=23|lrH-C=60| |lrH-V=24|lrH-E=48|lrH-F=18|lrH-Fdetail=12{4}+6{8}| |lrH-chi=-6|lrH-group=Oh| |lrH-B=Sroh|

|grH-name=Great rhombihexahedron| |grH-image=Great rhombihexahedron.png| |grH-vfigimage=Great rhombihexahedron_vertfig.png|grH-vfig=4.8/3.4.8/3| |grH-Wythoff=2 3/2 4/3 |
or 2 4/3 4/2| |grH-W=103|grH-U=21|grH-K=26|grH-C=82| |grH-V=24|grH-E=48|grH-F=18|grH-Fdetail=12{4}+6{8/3}| |grH-chi=-6|grH-group=Oh| |grH-B=Groh|

|ctCO-name=Cubitruncated cuboctahedron| |ctCO-image=Cubitruncated cuboctahedron.png| |ctCO-vfigimage=Cubitruncated cuboctahedron_vertfig.png|ctCO-vfig=6.8.8/3| |ctCO-altname1=Cuboctatruncated cuboctahedron| |ctCO-Wythoff=3 44/3 | | |ctCO-W=79|ctCO-U=16|ctCO-K=21|ctCO-C=52| |ctCO-V=48|ctCO-E=72|ctCO-F=20|ctCO-Fdetail=8{6}+6{8}+6{8/3}| |ctCO-chi=-4|ctCO-group=Oh| |ctCO-B=Cotco|

|grID-name=Great rhombicosidodecahedron| |grID-image=Great rhombicosidodecahedron.png| |grID-vfigimage=Great rhombicosidodecahedron vertfig.png|grID-vfig=4.6.10| |grID-altname1=Rhombitruncated icosidodecahedron| |grID-altname2=Truncated icosidodecahedron| |grID-Wythoff=2 3 5 | | |grID-W=16|grID-U=28|grID-K=33|grID-C=31| |grID-V=120|grID-E=180|grID-F=62|grID-Fdetail=30{4}+20{6}+12{10}| |grID-chi=2|grID-group=Ih| |grID-B=Grid|

|gtID-name=Great truncated icosidodecahedron| |gtID-image=Great truncated icosidodecahedron.png| |gtID-vfigimage=Great truncated icosidodecahedron_vertfig.png|gtID-vfig=4.6.10/3| |gtID-altname1=Great quasitruncated icosidodecahedron| |gtID-Wythoff=2 35/3 | | |gtID-W=108|gtID-U=68|gtID-K=73|gtID-C=87| |gtID-V=120|gtID-E=180|gtID-F=62|gtID-Fdetail=30{4}+20{6}+12{10/3}| |gtID-chi=2|gtID-group=Ih| |gtID-B=Gaquatid|

|rI-name=Rhombicosahedron| |rI-image=Rhombicosahedron.png| |rI-vfigimage=Rhombicosahedron_vertfig.png|rI-vfig=4.6.4.6| |rI-Wythoff=2 35/2 | | |rI-W=96|rI-U=56|rI-K=61|rI-C=72| |rI-V=60|rI-E=120|rI-F=50|rI-Fdetail=30{4}+20{6}| |rI-chi=-10|rI-group=Ih| |rI-B=Ri|

|grD-name=Great rhombidodecahedron| |grD-image=Great rhombidodecahedron.png| |grD-vfigimage=Great rhombidodecahedron_vertfig.png|grD-vfig=4.10/3.4.10/3| |grD-Wythoff=2 3/25/3 | | |grD-W=109|grD-U=73|grD-K=78|grD-C=89| |grD-V=60|grD-E=120|grD-F=42|grD-Fdetail=30{4}+12{10/3}| |grD-chi=-18|grD-group=Ih| |grD-B=Gird|

|itDD-name=Icositruncated dodecadodecahedron| |itDD-image=Icositruncated dodecadodecahedron.png| |itDD-vfigimage=Icositruncated dodecadodecahedron_vertfig.png|itDD-vfig=6.10.10/3| |itDD-altname1=Icosidodecatruncated icosidodecahedron| |itDD-Wythoff=3 55/3 | | |itDD-W=84|itDD-U=45|itDD-K=50|itDD-C=57| |itDD-V=120|itDD-E=180|itDD-F=44|itDD-Fdetail=20{6}+12{10}+12{10/3}| |itDD-chi=-16|itDD-group=Ih| |itDD-B=Idtid|

|gDI-name=Great dodecicosahedron| |gDI-image=Great dodecicosahedron.png| |gDI-vfigimage=Great dodecicosahedron_vertfig.png|gDI-vfig=6.10/3.6.10/3| |gDI-Wythoff=3 5/35/2 | | |gDI-W=101|gDI-U=63|gDI-K=68|gDI-C=79| |gDI-V=60|gDI-E=120|gDI-F=32|gDI-Fdetail=20{6}+12{10/3}| |gDI-chi=-28|gDI-group=Ih| |gDI-B=Giddy|

|tDD-name=Truncated dodecadodecahedron| |tDD-image=Truncated dodecadodecahedron.png| |tDD-vfigimage=Truncated dodecadodecahedron_vertfig.png|tDD-vfig=4.10.10/3| |tDD-altname1=Quasitruncated dodecahedron| |tDD-Wythoff=2 55/3 | | |tDD-W=98|tDD-U=59|tDD-K=64|tDD-C=75| |tDD-V=120|tDD-E=180|tDD-F=54|tDD-Fdetail=30{4}+12{10}+12{10/3}| |tDD-chi=-6|tDD-group=Ih| |tDD-B=Quitdid|

|lrD-name=Small rhombidodecahedron| |lrD-image=Small rhombidodecahedron.png| |lrD-vfigimage=Small rhombidodecahedron_vertfig.png|lrD-vfig=4.10.4.10| |lrD-Wythoff=25/25 | | |lrD-W=74|lrD-U=39|lrD-K=44|lrD-C=46| |lrD-V=60|lrD-E=120|lrD-F=42|lrD-Fdetail=30{4}+12{10}| |lrD-chi=-18|lrD-group=Ih| |lrD-B=Sird|

|lDI-name=Small dodecicosahedron| |lDI-image=Small dodecicosahedron.png| |lDI-vfigimage=Small dodecicosahedron_vertfig.png|lDI-vfig=6.10.6.10| |lDI-Wythoff=3 3/2 5 | | |lDI-W=90|lDI-U=50|lDI-K=55|lDI-C=64| |lDI-V=60|lDI-E=120|lDI-F=32|lDI-Fdetail=20{6}+12{10}| |lDI-chi=-28|lDI-group=Ih| |lDI-B=Siddy|

|lIID-name=Small icosicosidodecahedron| |lIID-image=Small icosicosidodecahedron.png| |lIID-vfigimage=Small icosicosidodecahedron_vertfig.png| |lIID-vfig=6.5/2.6.3| |lIID-Wythoff=5/2 3 | 3| |lIID-W=71|lIID-U=31|lIID-K=36|lIID-C=40| |lIID-V=60|lIID-E=120|lIID-F=52| |lIID-Fdetail=20{3}+12{5/2}+20{6}| |lIID-chi=-8|lIID-group=Ih| |lIID-B=Siid|

|rDD-name=Rhombidodecadodecahedron| |rDD-image=Rhombidodecadodecahedron.png| |rDD-vfigimage=Rhombidodecadodecahedron_vertfig.png| |rDD-vfig=4.5/2.4.5| |rDD-Wythoff=5/2 5 | 2| |rDD-W=76|rDD-U=38|rDD-K=43|rDD-C=48| |rDD-V=60|rDD-E=120|rDD-F=54| |rDD-Fdetail=30{4}+12{5}+12{5/2}| |rDD-chi=-6|rDD-group=Ih| |rDD-B=Raded|

|gCCO-name=Great cubicuboctahedron| |gCCO-image=Great cubicuboctahedron.png| |gCCO-vfigimage=Great cubicuboctahedron_vertfig.png| |gCCO-vfig=4.5/2.4.5| |gCCO-Wythoff=3 4 | 4/3| |gCCO-W=77|gCCO-U=14|gCCO-K=19|gCCO-C=50| |gCCO-V=24|gCCO-E=48|gCCO-F=20| |gCCO-Fdetail=8{3}+6{4}+6{8/3}| |gCCO-chi=-4|gCCO-group=Oh| |gCCO-B=Gocco|

|gdDID-name=Great ditrigonal dodecicosidodecahedron| |gdDID-image=Great ditrigonal dodecicosidodecahedron.png| |gdDID-vfigimage=Great ditrigonal dodecicosidodecahedron_vertfig.png| |gdDID-vfig=4.5/2.4.5| |gdDID-Wythoff=3 5 | 5/3| |gdDID-W=81|gdDID-U=42|gdDID-K=47|gdDID-C=54| |gdDID-V=60|gdDID-E=120|gdDID-F=44| |gdDID-Fdetail=20{3}+12{5}+12{10/3}| |gdDID-chi=-16|gdDID-group=Ih| |gdDID-B=Gidditdid|

|gDID-name=Great dodecicosidodecahedron| |gDID-image=Great dodecicosidodecahedron.png| |gDID-vfigimage=Great dodecicosidodecahedron_vertfig.png| |gDID-vfig=4.5/2.4.5| |gDID-Wythoff=5/2 3 | 5/3| |gDID-W=99|gDID-U=61|gDID-K=66|gDID-C=77| |gDID-V=60|gDID-E=120|gDID-F=44| |gDID-Fdetail=20{3}+12{5/2}+12{10/3}| |gDID-chi=-16|gDID-group=Ih| |gDID-B=Gaddid|

|nCO-name=Snub cube| |nCO-image=Snub hexahedron.png| |nCO-vfigimage=Snub_cube_vertfig.png| |nCO-vfig=3.3.3.3.4| |nCO-Wythoff=| 2 3 4| |nCO-W=17|nCO-U=12|nCO-K=17|nCO-C=24| |nCO-V=24|nCO-E=60|nCO-F=38| |nCO-Fdetail=(8+24){3}+6{4}| |nCO-chi=2|nCO-group=O| |nCO-B=Snic|

|nID-name=Snub dodecahedron| |nID-image=Snub dodecahedron ccw.png| |nID-vfigimage=Snub_dodecahedron_vertfig.png| |nID-vfig=3.3.3.3.5| |nID-Wythoff=| 2 3 5| |nID-W=18|nID-U=29|nID-K=34|nID-C=32| |nID-V=60|nID-E=150|nID-F=92| |nID-Fdetail=(20+60){3}+12{5}| |nID-chi=2| |nID-group=I| |nID-B=Snid|

}}

Template documentation[view] [edit] [history] [purge]

{{polyhedra DB}} — A database of information about different polyhedra.

Usage[edit]

{{Polyhedra DB
  |Template used to display the information #REQUIRED
  |Short form name #REQUIRED
}}

Display templates[edit]

The first argument to the template tag should be the name of a second template used to display information about an individual polyhedron. Possible arguments are:

Template:Polyhedra smallbox2
Displays the polyhedron in a small box, intended to be used inside a table

Short names of Polyhedron[edit]

The naming system follows the names used for the polyhedron but they have been shortend.

  • T - tetrahedron or Tetra
  • O - octahedron or Octa
  • C - Cube
  • D - Dodecahedron or Dodeca
  • I - Icosahedron or Icosi
  • r - rhombi
  • s - stelated
  • g - great
  • t - truncated
  • l - small (lesser) used to avoid naming conflict
  • d - ditrigonal
  • h - hemi
  • u - uniform
  • n - snub (n is used to avoid name conflict)

So gtCO becomes great truncated CubeOctahedron.

Properties defined[edit]

For each polyhedron the following properties are defined.

Here the initial T is replaced by the name of the each polyhedron

  • T-name=Tetrahedron - the name used in Wikipedia for the polyhedron
  • stH-altname1=Quasitruncated hexahedron - alternate name for the polyhedron (optional)
  • stH-altname2=stellatruncated cube - second alternate name (optional)
  • T-image=tetrahedron.jpg - image of the polyhedron
  • T-Wythoff=3|3 2 - Wythoff symbol
  • T-W=1 - number used in Polyhedron Models, by Magnus Wenninger.
  • T-U=01 - Uniform indexing: U01-U80 (Tetrahedron first, Prisms at 76+)
  • T-K=06 - Kaleido indexing: K01-K80 <K(n)=U(n-5) for n=6..80> (prisms 1-5, Tetrahedron 6+)
  • T-C=15 - Number used in Coexeter et al. -
  • T-V=4 - Number of vertices
  • T-E=6 - Number of edges
  • T-F=4 - Number of faces
  • T-Fdetail=4{3} - Number{type} of faces
  • T-chi=2 - Euler characteristic
  • T-vfig=3.3.3 - Vertex figure
  • T-vfigimage=tetrahedron_vertfig.png - image of vertex figure
  • T-group=Td - Symmetry group
  • T-B=Tet - Bowers name

Example[edit]

Code Result
{{Polyhedra DB|Polyhedra smallbox2|T}}
Tetrahedron.png

Tetrahedron
Tet
V 4,E 6,F 4=4{3}
χ=2, group=Td
3 | 3 2 - 3.3.3
W1, U01, K06, C15

Full list of names available[edit]

  • T - Tetrahedron - Tet
  • O - Octahedron - Oct
  • C - Hexahedron - Cube
  • I - Icosahedron - Ike
  • D - Dodecahedron - Doe
  • gI - Great icosahedron - Gike
  • gD - Great dodecahedron - Gad
  • lsD - Small stellated dodecahedron - Sissid
  • gsD - Great stellated dodecahedron - Gissid
  • CO - Cuboctahedron - Co
  • ID - Icosidodecahedron - Id
  • gID - Great icosidodecahedron - Gid
  • DD - Dodecadodecahedron - Did
  • ldID - Small ditrigonal icosidodecahedron - Sidtid
  • dDD - Ditrigonal dodecadodecahedron - Ditdid
  • gdID - Great ditrigonal icosidodecahedron - Gidtid
  • tT - Truncated tetrahedron - Tut
  • tO - Truncated octahedron - Toe
  • tC - Truncated cube - Tic
  • tI - Truncated icosahedron - Ti
  • tD - Truncated dodecahedron - Tid
  • tgD - Truncated great dodecahedron - Tigid
  • gtI - Truncated great icosahedron - Tiggy
  • stH - Stellated truncated hexahedron - Quith
  • lstD - Small stellated truncated dodecahedron - Quitsissid
  • gstD - Great stellated truncated dodecahedron - Quitgissid
  • ThH - Tetrahemihexahedron - Thah
  • OhO - Octahemioctahedron - Oho
  • ChO - Cubohemioctahedron - Cho
  • lIhD - Small icosihemidodecahedron - Seihid
  • lDhD - Small dodecahemidodecahedron - Sidhid
  • gIhD - Great icosihemidodecahedron - Geihid
  • gDhD - Great dodecahemidodecahedron - Gidhid
  • gDhI - Great dodecahemicosahedron - Gidhei
  • lDhI - Small dodecahemicosahedron - Sidhei
  • lrCO - Small rhombicuboctahedron - Sirco
  • lCCO - Small cubicuboctahedron - Socco
  • ugrCO - Uniform great rhombicuboctahedron - Querco
  • lrID - Small rhombicosidodecahedron - Srid
  • lDID - Small dodecicosidodecahedron - Saddid
  • ugrID - Uniform great rhombicosidodecahedron - Qrid
  • gIID - Great icosicosidodecahedron - Giid
  • ldDID - Small ditrigonal dodecicosidodecahedron - Sidditdid
  • IDD - Icosidodecadodecahedron - Ided
  • grCO - Great rhombicuboctahedron - Girco
  • gtCO - Great truncated cuboctahedron - Quitco
  • ctCO - Cubitruncated cuboctahedron - Cotco
  • grID - Great rhombicosidodecahedron - Grid
  • gtID - Great truncated icosidodecahedron - Gaquatid
  • itDD - Icositruncated dodecadodecahedron - Idtid
  • tDD - Truncated dodecadodecahedron - Quitdid
  • lrH - Small rhombihexahedron - Sroh
  • grH - Great rhombihexahedron - Groh
  • rI - Rhombicosahedron - Ri
  • grD - Great rhombidodecahedron - Gird
  • gDI - Great dodecicosahedron - Giddy
  • lrD - Small rhombidodecahedron - Sird
  • lDI - Small dodecicosahedron - Siddy

How it works[edit]

Each polyhedron is included with code like

{{Polyhedra DB|Polyhedra smallbox2|T}}

Where Polyhedra DB is a template containg all the data. Polyhedra smallbox2 is a template for displaying the data and T is the name of the polyhedra, in this case Tetrahedron.

Template:Polyhedra DB is like

{{{{{1}}}|{{{2}}}|

|T-name=Tetrahedron|T-image=tetrahedron.jpg|T-Wythoff=3|3 2|
|T-W=1|T-U=01|T-K=06|T-C=15|T-V=4|T-E=6|T-F=4|T-Fdetail=4{3}|T-chi=2|
|T-vfig=3.3.3|T-vfigimage=tetrahedron_vertfig.png|T-group=T<sub>d</sub>|

|O-name=Octahedron|O-image=octahedron.jpg|O-Wythoff=4|3 2|
...
}}

The first two parameters to this template just pass their arguments through, so this resolves to

{{Polyhedra smallbox2|T|T-name=Tetrahedron|....}}

and means that the Polyhedra smallbox2 template is called. Each variable in this template is of the form X-name where X is a short name for the polyhedron.

Template:Polyhedra smallbox2 is like

[[Image:{{{{{{1}}}-image}}}|100px]]<BR>
[[{{{{{{1}}}-name}}}]]<BR>
V {{{{{{1}}}-V}}},E {{{{{{1}}}-E}}},F {{{{{{1}}}-F}}}={{{{{{1}}}-Fdetail}}}
<br>''χ''={{{{{{1}}}-chi}}}, group={{{{{{1}}}-group}}}
<BR>{{{{{{1}}}-Wythoff}}} - {{{{{{1}}}-vfig}}}
<BR>W{{{{{{1}}}-W}}}, U{{{{{{1}}}-U}}}, K{{{{{{1}}}-K}}}, C{{{{{{1}}}-C}}}
<br>{{{{{{1}}}-altname|}}}

Occurrences of {{{1}}} are replaced by the first parameter. In this case T so after substituting the variable it becomes

[[Image:{{{T-image}}}|100px]]<BR>
[[{{{T-name}}}]]<BR>
V {{{T-V}}},E {{{T-E}}},F {{{T-F}}}={{{T-Fdetail}}}
<br>''χ''={{{T-chi}}}, group={{{T-group}}}
<BR>{{{{T-Wythoff}}} - {{{T-vfig}}}
<BR>W{{{{T-W}}}, U{{{T-U}}}, K{{{T-K}}}, C{{{T-C}}}
<br>{{{T-altname|}}}

Finally {{{T-image}}} and {{{T-name}}} just select the other parameters from the Polyhedra DB so this now just like an infobox template.

See also[edit]