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

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

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

@scrappapertiger.bsky.social made a modular origami buckyball! #truncatedIcosahedron #polyhedra

#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

I posted how I'm struggling to fold some origami models of complex polyhedra.

I have an idea which involved folding them from tracing paper.

I've folded them before, using 200gsm watercolour paper.

When that paper is coated with cyanotype before folding, you can get a metamorphogram.

Here's John Montroll's 'Gamma Star' during exposure, and as a final image.

#origami #polyhedra #JohnMontroll #GammaStar #polyhedron #folding #FoldingPaper #cyanotype
#blueprint #metamorphogram #memory

Pattern and chaos.

Here's the crease pattern in paper for John Montroll's Dimpled Snub Cube.

And then there's the chaotic failed collapse of it into a 3D shape.

I've folded these before, and it's an interesting fight, wrestling a sheet of paper into form.

Practice makes polyhedra.

Sometimes things fail.

I've been trying to get back into origami practice with John Montroll's - 'A Constellation of Origami Polyhedra' (https://johnmontroll.com/books/a-constellation-of-origami-polyhedra/).

Using 75 cm squares of tracing paper made it harder - wrong paper for these models.

The crease patterns are beautiful - this is for a Sunken Cuboctohedron. But I've failed to fully fold them into 3D shape.

But it's OK. Sometimes things fail.