Template:Semireg polyhedra db: Difference between revisions
ABCH |
dihedral angles from Williams |
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Line 14: | Line 14: | ||
|tT-B=Tut|tT-special=|tT-schl=t{3,3}| |
|tT-B=Tut|tT-special=|tT-schl=t{3,3}| |
||
|tT-dual=Triakis tetrahedron| |
|tT-dual=Triakis tetrahedron| |
||
|tT-dihedral=| |
|tT-dihedral=3-6:109°28'16"<BR>6-6:70°31'44"| |
||
|tT-CD={{CDD|node_1|3|node_1|3|node}} |
|tT-CD={{CDD|node_1|3|node_1|3|node}} |
||
Line 33: | Line 33: | ||
|tO-schl=t<sub>0,1</sub>{3,4}<BR>t<sub>0,1,2</sub>{3,3}|tO-schl2=and <math>t\begin{Bmatrix} 3 \\ 3 \end{Bmatrix}</math>| |
|tO-schl=t<sub>0,1</sub>{3,4}<BR>t<sub>0,1,2</sub>{3,3}|tO-schl2=and <math>t\begin{Bmatrix} 3 \\ 3 \end{Bmatrix}</math>| |
||
|tO-dual=Tetrakis hexahedron| |
|tO-dual=Tetrakis hexahedron| |
||
|tO-dihedral=4-6:cos(-1/sqrt(3))=125°15'51"<BR>6-6:cos(-1/3)=109°28'16"| |
|||
|tO-dihedral=| |
|||
|tO-CD={{CDD|node|4|node_1|3|node_1}}<BR>{{CDD|node_1|3|node_1|3|node_1}} |
|tO-CD={{CDD|node|4|node_1|3|node_1}}<BR>{{CDD|node_1|3|node_1|3|node_1}} |
||
Line 50: | Line 50: | ||
|tC-B=Tic| |
|tC-B=Tic| |
||
|tC-dual=Triakis octahedron|tC-schl=t{4,3}| |
|tC-dual=Triakis octahedron|tC-schl=t{4,3}| |
||
|tC-dihedral=| |
|tC-dihedral=3-8:125°15'51"<BR>8-8:90°| |
||
|tC-special=| |
|tC-special=| |
||
|tC-CD={{CDD|node_1|4|node_1|3|node}} |
|tC-CD={{CDD|node_1|4|node_1|3|node}} |
||
Line 67: | Line 67: | ||
|tI-B=Ti| |
|tI-B=Ti| |
||
|tI-dual=Pentakis dodecahedron|tI-schl=t{3,5}| |
|tI-dual=Pentakis dodecahedron|tI-schl=t{3,5}| |
||
|tI-dihedral= |
|tI-dihedral=6-6: 138.189685°<BR>6-5: 142.62° |
||
|tI-special=| |
|tI-special=| |
||
|tI-CD={{CDD|node|5|node_1|3|node_1}} |
|tI-CD={{CDD|node|5|node_1|3|node_1}} |
||
Line 84: | Line 84: | ||
|tD-B=Tid| |
|tD-B=Tid| |
||
|tD-dual=Triakis icosahedron|tD-schl=t{5,3}| |
|tD-dual=Triakis icosahedron|tD-schl=t{5,3}| |
||
|tD-dihedral= |
|tD-dihedral=10-10: 116.57<BR>3-10: 142.62| |
||
|tD-special=| |
|tD-special=| |
||
|tD-CD={{CDD|node_1|5|node_1|3|node}} |
|tD-CD={{CDD|node_1|5|node_1|3|node}} |
||
Line 135: | Line 135: | ||
|grCO-B=Girco|grCO-special=[[zonohedron]]|grCO-schl=t<sub>0,1,2</sub>{4,3}|grCO-schl2=<math>t\begin{Bmatrix} 3 \\ 4 \end{Bmatrix}</math>| |
|grCO-B=Girco|grCO-special=[[zonohedron]]|grCO-schl=t<sub>0,1,2</sub>{4,3}|grCO-schl2=<math>t\begin{Bmatrix} 3 \\ 4 \end{Bmatrix}</math>| |
||
|grCO-dual=Disdyakis dodecahedron| |
|grCO-dual=Disdyakis dodecahedron| |
||
|grCO-dihedral=4-6:cos(-sqrt(6)/3)=144°44'08"<BR>4-8:cos(-sqrt(2)/3)=135°<BR>6-8:cos(-sqrt(3)/3)=125°15'51"| |
|||
|grCO-dihedral=| |
|||
|grCO-CD={{CDD|node_1|4|node_1|3|node_1}} |
|grCO-CD={{CDD|node_1|4|node_1|3|node_1}} |
||
Line 153: | Line 153: | ||
|grID-B=Grid|grID-special=[[zonohedron]]||grID-schl=t<sub>0,1,2</sub>{5,3}|grID-schl2=<math>t\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}</math>| |
|grID-B=Grid|grID-special=[[zonohedron]]||grID-schl=t<sub>0,1,2</sub>{5,3}|grID-schl2=<math>t\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}</math>| |
||
|grID-dual=Disdyakis triacontahedron| |
|grID-dual=Disdyakis triacontahedron| |
||
|grID-dihedral= |
|grID-dihedral=6-10: 142.62°<BR>4-10: 148.28°<BR>4-6: 159.095°| |
||
|grID-CD={{CDD|node_1|5|node_1|3|node_1}} |
|grID-CD={{CDD|node_1|5|node_1|3|node_1}} |
||
Line 170: | Line 170: | ||
|lrCO-B=Sirco| |
|lrCO-B=Sirco| |
||
|lrCO-dual=Deltoidal icositetrahedron| |
|lrCO-dual=Deltoidal icositetrahedron| |
||
|lrCO-dihedral=| |
|lrCO-dihedral=3-4:144°44'08"<BR>4-4:135°| |
||
|lrCO-special=|lrCO-schl=t<sub>0,2</sub>{4,3}|lrCO-schl2=<math>r\begin{Bmatrix} 3 \\ 4 \end{Bmatrix}</math>| |
|lrCO-special=|lrCO-schl=t<sub>0,2</sub>{4,3}|lrCO-schl2=<math>r\begin{Bmatrix} 3 \\ 4 \end{Bmatrix}</math>| |
||
|lrCO-CD={{CDD|node_1|4|node|3|node_1}} |
|lrCO-CD={{CDD|node_1|4|node|3|node_1}} |
||
Line 188: | Line 188: | ||
|lrID-B=Srid| |
|lrID-B=Srid| |
||
|lrID-dual=Deltoidal hexecontahedron| |
|lrID-dual=Deltoidal hexecontahedron| |
||
|lrID-dihedral=| |
|lrID-dihedral=3-4:159°05'41"<BR>4-5:148°16'57"| |
||
|lrID-special=|lrID-schl=t<sub>0,2</sub>{5,3}|lrID-schl2=<math>r\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}</math>| |
|lrID-special=|lrID-schl=t<sub>0,2</sub>{5,3}|lrID-schl2=<math>r\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}</math>| |
||
|lrID-CD={{CDD|node_1|5|node|3|node_1}} |
|lrID-CD={{CDD|node_1|5|node|3|node_1}} |
||
Line 206: | Line 206: | ||
|nCO-B=Snic|nCO-special=[[chirality (mathematics)|chiral]]| |
|nCO-B=Snic|nCO-special=[[chirality (mathematics)|chiral]]| |
||
|nCO-dual=Pentagonal icositetrahedron| |
|nCO-dual=Pentagonal icositetrahedron| |
||
|nCO-dihedral=| |
|nCO-dihedral=3-3: 153°14'04"<BR>3-4:142°59'00"| |
||
|nCO-special=[[chirality (mathematics)|chiral]]|nCO-schl=s{4,3}|nCO-schl2=<math>s\begin{Bmatrix} 3 \\ 4 \end{Bmatrix}</math>| |
|nCO-special=[[chirality (mathematics)|chiral]]|nCO-schl=s{4,3}|nCO-schl2=<math>s\begin{Bmatrix} 3 \\ 4 \end{Bmatrix}</math>| |
||
|nCO-CD={{CDD|node_h|4|node_h|3|node_h}} |
|nCO-CD={{CDD|node_h|4|node_h|3|node_h}} |
||
Line 224: | Line 224: | ||
|nID-B=Snid|nID-special=[[chirality (mathematics)|chiral]]|nID-schl=s{5,3}|nID-schl2=<math>s\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}</math>| |
|nID-B=Snid|nID-special=[[chirality (mathematics)|chiral]]|nID-schl=s{5,3}|nID-schl2=<math>s\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}</math>| |
||
|nID-dual=Pentagonal hexecontahedron| |
|nID-dual=Pentagonal hexecontahedron| |
||
|nID-dihedral=| |
|nID-dihedral=3-3:164°10'31"<BR>3-5:152°55'53"| |
||
|nID-CD={{CDD|node_h|5|node_h|3|node_h}} |
|nID-CD={{CDD|node_h|5|node_h|3|node_h}} |
||
Revision as of 02:45, 8 April 2012
{{{{{1}}}|{{{2}}}|
|tT-name=Truncated tetrahedron|
|tT-image=Truncated tetrahedron.png|
|tT-image2=Truncatedtetrahedron.jpg|
|tT-image3=Truncatedtetrahedron.gif|
|tT-dimage=Triakistetrahedron.jpg|
|tT-vfigimage=Truncated tetrahedron vertfig.png|tT-netimage=Truncated tetrahedron flat.svg|
|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
A3, [3,3], (*332)|
|tT-B=Tut|tT-special=|tT-schl=t{3,3}|
|tT-dual=Triakis tetrahedron|
|tT-dihedral=3-6:109°28'16"
6-6:70°31'44"|
|tT-CD=
|tO-name=Truncated octahedron|
|tO-image=Truncated octahedron.png|
|tO-image2=Truncatedoctahedron.jpg|
|tO-image3=Truncatedoctahedron.gif|
|tO-dimage=Tetrakishexahedron.jpg|
|tO-vfigimage=Truncated octahedron vertfig.png|tO-netimage=Truncated Octahedron Net.svg|
|tO-vfig=4.6.6|
|tO-Wythoff=2 4 | 3
3 3 2 ||
|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
BC3, [4,3], (*432)
Th, [3,3] and (*332)|
|tO-B=Toe|
|tO-special=zonohedron
permutohedron|
|tO-schl=t0,1{3,4}
t0,1,2{3,3}|tO-schl2=and |
|tO-dual=Tetrakis hexahedron|
|tO-dihedral=4-6:cos(-1/sqrt(3))=125°15'51"
6-6:cos(-1/3)=109°28'16"|
|tO-CD=
|tC-name=Truncated cube|
|tC-altname1=Truncated hexahedron|
|tC-image=Truncated hexahedron.png|
|tC-image2=Truncatedhexahedron.jpg|
|tC-image3=Truncatedhexahedron.gif|
|tC-dimage=Triakisoctahedron.jpg|
|tC-vfigimage=Truncated cube vertfig.png|tC-netimage=Truncated hexahedron flat.svg|
|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
BC3, [4,3], (*432)|
|tC-B=Tic|
|tC-dual=Triakis octahedron|tC-schl=t{4,3}|
|tC-dihedral=3-8:125°15'51"
8-8:90°|
|tC-special=|
|tC-CD=
|tI-name=Truncated icosahedron|
|tI-image=Truncated icosahedron.png|
|tI-image2=Truncatedicosahedron.jpg|
|tI-image3=Truncatedicosahedron.gif|
|tI-dimage=Pentakisdodecahedron.jpg|
|tI-vfigimage=Truncated icosahedron vertfig.png|tI-netimage=Truncated icosahedron flat.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
H3, [5,3], (*532)|
|tI-B=Ti|
|tI-dual=Pentakis dodecahedron|tI-schl=t{3,5}|
|tI-dihedral=6-6: 138.189685°
6-5: 142.62°
|tI-special=|
|tI-CD=
|tD-name=Truncated dodecahedron|
|tD-image=Truncated dodecahedron.png|
|tD-image2=Truncateddodecahedron.jpg|
|tD-image3=Truncateddodecahedron.gif|
|tD-dimage=Triakisicosahedron.jpg|
|tD-vfigimage=Truncated dodecahedron vertfig.png|tD-netimage=Truncated dodecahedron flat.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
H3, [5,3], (*532)|
|tD-B=Tid|
|tD-dual=Triakis icosahedron|tD-schl=t{5,3}|
|tD-dihedral=10-10: 116.57
3-10: 142.62|
|tD-special=|
|tD-CD=
|CO-name=Cuboctahedron|
|CO-image=Cuboctahedron.png|
|CO-image2=Cuboctahedron.jpg|
|CO-image3=Cuboctahedron.gif|
|CO-dimage=Rhombicdodecahedron.jpg|
|CO-vfigimage=Cuboctahedron_vertfig.png|CO-netimage=Cuboctahedron flat.svg|
|CO-vfig=3.4.3.4|
|CO-Wythoff=2 | 3 4
3 3 | 2|
|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
BC3, [4,3], (*432)
Td, [3,3], (*332)|
|CO-B=Co|CO-special=quasiregular|
|CO-dual=Rhombic dodecahedron|CO-schl=t1{4,3}
t0,2{3,3}|
|CO-dihedral=125.26°
|
|CO-CD=
|ID-name=Icosidodecahedron|
|ID-image=Icosidodecahedron.png|
|ID-image2=Icosidodecahedron.jpg|
|ID-image3=Icosidodecahedron.gif|
|ID-dimage=Rhombictriacontahedron.svg|
|ID-vfigimage=Icosidodecahedron_vertfig.png|ID-netimage=Icosidodecahedron_flat.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
H3, [5,3], (*532)|
|ID-B=Id||ID-special=quasiregular|
|ID-dual=Rhombic triacontahedron|ID-schl=t1{5,3}|ID-schl2=|
|ID-dihedral=142.62°
|
|ID-CD=
|grCO-name=Truncated cuboctahedron|
|grCO-image=Great rhombicuboctahedron.png|
|grCO-image2=Truncatedcuboctahedron.jpg|
|grCO-image3=Truncatedcuboctahedron.gif|
|grCO-dimage=Disdyakisdodecahedron.jpg|
|grCO-vfigimage=Great rhombicuboctahedron vertfig.png|grCO-netimage=Truncated cuboctahedron flat.svg|
|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
BC3, [4,3], (*432)|
|grCO-B=Girco|grCO-special=zonohedron|grCO-schl=t0,1,2{4,3}|grCO-schl2=|
|grCO-dual=Disdyakis dodecahedron|
|grCO-dihedral=4-6:cos(-sqrt(6)/3)=144°44'08"
4-8:cos(-sqrt(2)/3)=135°
6-8:cos(-sqrt(3)/3)=125°15'51"|
|grCO-CD=
|grID-name=Truncated icosidodecahedron|
|grID-image=Great rhombicosidodecahedron.png|
|grID-image2=Truncatedicosidodecahedron.jpg|
|grID-image3=Truncatedicosidodecahedron.gif|
|grID-dimage=Disdyakistriacontahedron.jpg|
|grID-vfigimage=Great rhombicosidodecahedron vertfig.png|grID-netimage=Truncated icosidodecahedron flat.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
H3, [5,3], (*532)|
|grID-B=Grid|grID-special=zonohedron||grID-schl=t0,1,2{5,3}|grID-schl2=|
|grID-dual=Disdyakis triacontahedron|
|grID-dihedral=6-10: 142.62°
4-10: 148.28°
4-6: 159.095°|
|grID-CD=
|lrCO-name=Rhombicuboctahedron|
|lrCO-altname1=Rhombicuboctahedron|
|lrCO-image=Small rhombicuboctahedron.png|
|lrCO-image2=Rhombicuboctahedron.jpg|
|lrCO-image3=Rhombicuboctahedron.gif|
|lrCO-dimage=Deltoidalicositetrahedron.jpg|
|lrCO-vfigimage=Small rhombicuboctahedron vertfig.png|lrCO-netimage=Rhombicuboctahedron flat.png|
|lrCO-vfig=3.4.4.4|
|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-group=Oh
BC3, [4,3], (*432)|
|lrCO-B=Sirco|
|lrCO-dual=Deltoidal icositetrahedron|
|lrCO-dihedral=3-4:144°44'08"
4-4:135°|
|lrCO-special=|lrCO-schl=t0,2{4,3}|lrCO-schl2=|
|lrCO-CD=
|lrID-name=Rhombicosidodecahedron|
|lrID-image=Small rhombicosidodecahedron.png|
|lrID-image2=Rhombicosidodecahedron.jpg|
|lrID-image3=Rhombicosidodecahedron.gif|
|lrID-dimage=Deltoidalhexecontahedron.jpg|
|lrID-altname1=Rhombicosidodecahedron|lrID-netimage=Rhombicosidodecahedron flat.png|
|lrID-vfig=3.4.5.4|
|lrID-vfigimage=Small rhombicosidodecahedron vertfig.png|
|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-group=Ih
H3, [5,3], (*532)|
|lrID-B=Srid|
|lrID-dual=Deltoidal hexecontahedron|
|lrID-dihedral=3-4:159°05'41"
4-5:148°16'57"|
|lrID-special=|lrID-schl=t0,2{5,3}|lrID-schl2=|
|lrID-CD=
|nCO-name=Snub cube|
|nCO-image=Snub hexahedron.png|
|nCO-image2=Snubhexahedroncw.jpg|
|nCO-image3=Snubhexahedroncw.gif|
|nCO-dimage=Pentagonalicositetrahedronccw.jpg|
|nCO-vfigimage=Snub cube vertfig.png|nCO-netimage=Snub cube flat.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
½BC3, [4,3]+, (432)|
|nCO-B=Snic|nCO-special=chiral|
|nCO-dual=Pentagonal icositetrahedron|
|nCO-dihedral=3-3: 153°14'04"
3-4:142°59'00"|
|nCO-special=chiral|nCO-schl=s{4,3}|nCO-schl2=|
|nCO-CD=
|nID-name=Snub dodecahedron|
|nID-image=Snub dodecahedron ccw.png|
|nID-image2=Snubdodecahedronccw.jpg|
|nID-image3=Snubdodecahedronccw.gif|
|nID-dimage=Pentagonalhexecontahedronccw.jpg|
|nID-vfigimage=Snub dodecahedron vertfig.png|nID-netimage=Snub dodecahedron flat.svg|
|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
½H3, [5,3]+, (532)|
|nID-B=Snid|nID-special=chiral|nID-schl=s{5,3}|nID-schl2=|
|nID-dual=Pentagonal hexecontahedron|
|nID-dihedral=3-3:164°10'31"
3-5:152°55'53"|
|nID-CD=
}}