I couldn’t resist making this in Geogebra: morphing between a regular icosahedron and a regular dodecahedron.

h/t @unnick https://mathstodon.xyz/@unnick@booping.synth.download/114350750053349050

3D print based on design by Tadeusz Dorozinski #math #mathart #stem #steam #geometry #polyhedra #3dprinting #3dprintedmath @thingiverse @cults3d

Graphic design of a Stewart star dodecahedral polytoroid and 3D print: design components: cubes, J92s, J5s, decagonal pyramids. #3dprintedmath #3dprinting #stem #steam #geometry #polyhedra #math #mathart #art

Kepler-Fathauer topographical walkabout dodecahedral polytorid inspired by mathematician and astronomer Johannes Kepler and mathematical artist Robert Fathauer #math #mathart #geometry #polyhedra

3D print of a Hart dodecahedral polyknot inspired by sculptor George Hart with graphic design #mathart #3dprinting #3dprintedmath #math #topology #knots #knottheory #geometry #polyhedra More of my math art can be seen at: https://sites.google.com/view/structuralgeometry/home?pli=1

a Truncated Icosahedral Crinklehedron #math #mathart #stem #steam #polyhedra #geometry

#Maths #mathematics #Math Truncated icosahedron mapped from a continuous polynomial: (y/ϕ+z/ϕ^3)^60+ (y/ϕ-z/ϕ^3)^60+((x+y+z)/ϕ^2)^60+((x+y-z)/ϕ^2)^60+ ((-x+y+z)/ϕ^2)^60+((-x+y-z)/ϕ^2)^60+(x/ϕ^3+z/ϕ)^60+(-x/ϕ^3+z/ϕ)^60+(x/ϕ+y/ϕ^3)^60+(-x/ϕ+y/ϕ^3)^60+((3/(4+3ϕ))(x+ϕy))^60+((3/(4+3ϕ))(x-ϕy))^60+((3/(4+3ϕ))(y+ϕz))^60+((3/(4+3ϕ))(y-ϕz))^60+((3/(4+3ϕ))(z+ϕx))^60+((3/(4+3ϕ))(z-ϕx))^60-1=0 where ϕ (the golden ratio) = (√5+1)/2. #polyhedra

Rhombicuboctahedron or expanded octahedron mapped from continuous polynomial x^60+y^60+z^60+.7071^60((x+y)^60+(x-y)^60+(y+z)^60+(y-z)^60+(z+x)^60+(z-x)^60)+.5469^60((x+y+z)^60+(x+y-z)^60+(x-y+z)^60+(-x+y+z)^60)-1=0. The polyhedron is an Archimedean solid and has 26 faces (8 equilateral triangle and 18 square) 24 vertices and 48 edges, each of length 2/(√2+1) units. #maths #mathematics #math #polyhedra

This illustration of a 38-sided space-filling polyhedron is great! https://wolfr.am/Engel-38

This is the largest number of sides known for any convex space-filing polyhedron. The theoretical upper bound is 92, given by https://arxiv.org/abs/0708.2114

Soft #toys and #polyhedra were bound to catch a mathematician's attention. Guess where this is from.

(hint: suicide )

Also, just polar bears. Cartesian ones were unavailable.

#TilingTuesday: #Tiling of 114 identical #toroid equilateral #polyhedra

Oh my, this is so lovely and fun!

https://andrewmarsh.com/software/poly3d-web/

Polyhedron generator: you start with a polyhedron and can apply all sorts of cool operations to make new ones.

It reminds me of the Java applets I made (20+ years ago!) that would apply a few operations -- truncation, expansion, snubification -- to the Platonic solids. I should dig those up and see if they still work. What I like about is that they animated the transition.

https://ddrake.prose.sh/choosing_tools

Cork icosahedron. Displayed here on a zebrawood reliquary. I keep thinking of different materials for the polyhedra.

Indigo ikat Octahedron. Another polyhedron made with fabric from a salvaged vintage kimono. Ikat is woven from pre-dyed cotton yarn.

I see a lot of icosahedra with numbers on the faces. I thought I would try engraving one of the wooden ones with those. I didn’t want it to be too plain. So, I made some knotwork to go around the numbers.

I have been playing with a different technique for making laser-cut polyhedra. In honor of spring, this Sakura Dodecahedron is made with salvaged fabric from a vintage silk kimono bearing a stylized cherry blossom theme.

Rhombicosahedron from 3 shapes.

Very much inspired by postings by @Albert

It's #TilingTuesday - today some #polyhedra - here I tile a cube from 8 identical pieces - each one dodecahedron and three halved bilunabirotundas. There are holes in the model, but actually these shapes can tile space.