Snubification

Author

Eric W. Weisstein
November 16, 2020

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Polyhedra/Snubification.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Snubification.html.

©2020 Wolfram Research, Inc. except for portions noted otherwise

Code

snubify[poly_,d_,rot_]:=poly/.Polygon[v_]:>RotateAboutAxis[
Polygon[d Unit[c=Centroid[v]]+#&/@v],c,rot]

Cube

PolyhedronData

PolyhedronData["SnubCube"]

SnubPolyhedron

Graphics3D[SnubPolyhedron[Cube[]]]

Package

r=Root[-11-44 #1-60 ((#1)^2)+32 ((#1)^3)+176 ((#1)^4)+192 ((#1)^5)+64 ((#1)^6)&,2];
θ=ArcCos[Root[-1-2 ((#1)^2)-4 ((#1)^4)+8 ((#1)^6)&,2]];

Show[Graphics3D[Snubify[Polyhedron[Cube],r,0]],Boxed->False]

Show[Graphics3D[Snubify[Polyhedron[Cube],r,Pi/4]],Boxed->False]

Show[Graphics3D[Snubify[Polyhedron[Cube],r,θ]],Boxed->False]

Dodecahedron

PolyhedronData

PolyhedronData["SnubDodecahedron"]

SnubPolyhedron

Graphics3D[SnubPolyhedron[Dodecahedron[]]]

Package

r=Root[630125-51896000 ((#1)^2)+1325073600 ((#1)^4)-15468736000 ((#1)^6)+95108400640 ((#1)^8)-330140037120 ((#1)^10)+674629492736 ((#1)^12)-850532761600 ((#1)^14)+704411402240 ((#1)^16)-397017088000 ((#1)^18)+143602483200 ((#1)^20)-31457280000 ((#1)^22)+2097152000 ((#1)^24)&,15];θ=ArcCos[Root[1-2996 ((#1)^2)+9520 ((#1)^4)-3840 ((#1)^6)-7680 ((#1)^8)+1024 ((#1)^10)+4096 ((#1)^12)&,8]];

Show[Graphics3D[Snubify[Polyhedron[Dodecahedron],r,θ]],Boxed->False]

Icosahedron

PolyhedronData

PolyhedronData["SnubIcosidodecahedron"]

SnubPolyhedron

Graphics3D[SnubPolyhedron[Icosahedron[]]]

Package

Octahedron

PolyhedronData

PolyhedronData["SnubOctahedron"]

SnubPolyhedron

Graphics3D[SnubPolyhedron[Octahedron[]]]

Package

Tetrahedron

PolyhedronData

PolyhedronData["SnubTetrahedron"]

SnubPolyhedron

Graphics3D[SnubPolyhedron[Tetrahedron[]]]

Package