Method of matched asymptotic expansions

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|dtT-name=Triakis tetrahedron|dtT-image=triakistetrahedron.jpg|dtT-image2=triakistetrahedron.jpg|dtT-image3=triakistetrahedron.gif|dtT-dimage=Truncated tetrahedron.png|dtT-netimage=triakistetrahedron_net.png| |dtT-Cox=Template:CDD |dtT-V=8|dtT-E=18|dtT-F=12|dtT-Vdetail=4{3}+4{6}|dtT-chi=2| |dtT-ffig=V3.6.6|dtT-ftype=isosceles triangle |dtT-group=T_d, A₃, [3,3], (*332)| |dtT-rotgroup=T, [3,3]⁺, (332)| |dtT-dual=Truncated tetrahedron|dtT-dihedral=129° 31' 16"
$\arccos (-\frac{7}{11})$| |dtT-special=

|dtC-name=Triakis octahedron|dtC-image=triakisoctahedron.jpg|dtC-image2=triakisoctahedron.jpg|dtC-image3=triakisoctahedron.gif|dtC-dimage=Truncated hexahedron.png|dtC-netimage=triakisoctahedron_net.png| |dtC-Cox=Template:CDD |dtC-V=14|dtC-E=36|dtC-F=24|dtC-Vdetail=8{3}+6{8}|dtC-chi=2| |dtC-ffig=V3.8.8|dtC-ftype=isosceles triangle |dtC-group=O_h, BC₃, [4,3], (*432)| |dtC-rotgroup=O, [4,3]⁺, (432)| |dtC-dual=Truncated cube|dtC-dihedral=147° 21' 0"
$\arccos (-\frac{3+8\sqrt{2}}{17})$| |dtC-special=

|dtO-name=Tetrakis hexahedron|dtO-image=tetrakishexahedron.jpg|dtO-image2=tetrakishexahedron.jpg|dtO-image3=tetrakishexahedron.gif|dtO-dimage=Truncated octahedron.png|dtO-netimage=tetrakishexahedron_net.png| |dtO-Cox=Template:CDD |dtO-V=14|dtO-E=36|dtO-F=24|dtO-Vdetail=6{4}+8{6}|dtO-chi=2| |dtO-ffig=V4.6.6|dtO-ftype=isosceles triangle |dtO-group=O_h, BC₃, [4,3], (*432)| |dtO-rotgroup=O, [4,3]⁺, (432)| |dtO-dual=Truncated octahedron|dtO-dihedral=143° 7' 48"
$\arccos (-\frac{4}{5})$| |dtO-special=

|dtD-name=Triakis icosahedron|dtD-image=triakisicosahedron.jpg|dtD-image2=triakisicosahedron.jpg|dtD-image3=triakisicosahedron.gif|dtD-dimage=Truncated dodecahedron.png|dtD-netimage=triakisicosahedron_net.png| |dtD-Cox=Template:CDD |dtD-V=32|dtD-E=90|dtD-F=60|dtD-Vdetail=20{3}+12{10}|dtD-chi=2| |dtD-ffig=V3.10.10|dtD-ftype=isosceles triangle |dtD-group=I_h, H₃, [5,3], (*532)| |dtD-rotgroup=I, [5,3]⁺, (532)| |dtD-dual=Truncated dodecahedron|dtD-dihedral=160° 36' 45"
$\arccos (-\frac{24+15\sqrt{5}}{61})$| |dtD-special=

|dtI-name=Pentakis dodecahedron|dtI-image=pentakisdodecahedron.jpg|dtI-image2=pentakisdodecahedron.jpg|dtI-image3=pentakisdodecahedron.gif|dtI-dimage=Truncated icosahedron.png|dtI-netimage=pentakisdodecahedron_net.png| |dtI-Cox=Template:CDD |dtI-V=32|dtI-E=90|dtI-F=60|dtI-Vdetail=20{6}+12{5}|dtI-chi=2| |dtI-ffig=V5.6.6|dtI-ftype=isosceles triangle |dtI-group=I_h, H₃, [5,3], (*532)| |dtI-rotgroup=I, [5,3]⁺, (532)| |dtI-dual=Truncated icosahedron|dtI-dihedral=156° 43' 7"
$\arccos (-\frac{80+9\sqrt{5}}{109})$| |dtI-special=

|dCO-name=Rhombic dodecahedron|dCO-image=rhombicdodecahedron.jpg|dCO-image2=rhombicdodecahedron.jpg|dCO-image3=rhombicdodecahedron.gif|dCO-dimage=cuboctahedron.png|dCO-netimage=rhombicdodecahedron_net.svg| |dCO-Cox=Template:CDD
Template:CDD |dCO-V=14|dCO-E=24|dCO-F=12|dCO-Vdetail=8{3}+6{4}|dCO-chi=2| |dCO-ffig=V3.4.3.4|dCO-ftype=rhombus |dCO-group=O_h, BC₃, [4,3], (*432)| |dCO-rotgroup=O, [4,3]⁺, (432)| |dCO-dual=Cuboctahedron|dCO-dihedral=120°| |dCO-special=edge-transitive, zonohedron

|dID-name=Rhombic triacontahedron|dID-image=rhombictriacontahedron.png|dID-image2=rhombictriacontahedron.svg|dID-image3=rhombictriacontahedron.gif|dID-dimage=icosidodecahedron.svg|dID-netimage=rhombictriacontahedron net.svg| |dID-Cox=Template:CDD |dID-V=32|dID-E=60|dID-F=30|dID-Vdetail=20{3}+12{5}|dID-chi=2| |dID-ffig=V3.5.3.5|dID-ftype=rhombus |dID-group=I_h, H₃, [5,3], (*532)| |dID-rotgroup=I, [5,3]⁺, (532)| |dID-dual=Icosidodecahedron|dID-dihedral=144°| |dID-special=edge-transitive, zonohedron

|dSD-name=Pentagonal hexecontahedron|dSD-image=Pentagonalhexecontahedron.jpg|dSD-image2=Pentagonalhexecontahedron.jpg|dSD-image3=Pentagonalhexecontahedronccw.gif|dSD-dimage=Snub_dodecahedron_ccw.png|dSD-netimage=Pentagonalhexecontahedron net.png| |dSD-Cox=Template:CDD |dSD-V=92|dSD-E=150|dSD-F=60|dSD-Vdetail=12 {5}
20+60 {3}|dSD-chi=2| |dSD-ffig=V3.3.3.3.5|dSD-ftype=irregular pentagon |dSD-group=I, ½H₃, [5,3]⁺, (532)| |dSD-rotgroup=I, [5,3]⁺, (532)| |dSD-dual=Snub dodecahedron|dSD-dihedral=153° 10' 43"| |dSD-special=chiral

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