Lmst

🚨 Polyhedra crashes over 80% in under an hour! 🚨

ZKJ collapsed from $1.90 to just $0.30 in a sudden sell-off - wiping out nearly all market cap. Both the team and Binance have issued statements, but questions remain. Here's everything we know so far: https://auriccrypto.com/news/breaking-polyhedra-network-zkj-crashes-80-in-an-hour/

#ZKJ #Polyhedra #Binance #Crash #Crypto

I needed a bpy refresher. So I made a script to generate some polyhedra that Blender apparently doesn't have (Maybe bc they are not regular). After some calculations, I made the pentagonal trapezohedron, the d10 die in RPG. #blender #polyhedra #polyhedron #nomxd #Tech-talk🐾

I’ve already shared a few photos taken last month with Mood.Camera, so here are the rest of the photos that I shared elsewhere last month:

One of these is available for any use for free, and can be found in much higher quality on my CC0 Licensed Photos page.

https://macmanx.com/2025/05/01/april-2025-in-photos/

#californiaBotanicGarden #food #gamera #gargoyles #godzilla #lego #monthInPhotos #polyhedra #starWars #ultraman

Purple and orange wildflowers in a green field.

The image shows a collection of toy figures arranged on a dark surface. From left to right: a silver Mechagodzilla with blue accens, a black Shin Godzilla with purple spines, a small colorful LEGO house with flowers and windows, a silver Ultraman Arc with blue accents, a white icy wolf-like creature, and a large Gamera figure. The toys appear to be positioned as if in a standoff, with the house in the middle of the figures.

This is a small die-cast toy car model on a wooden surface, a gray Toyota Prius Prime with a hatchback design. The car has black windows and silver wheel rims. The model sits on a light brown wooden table with a beige wall visible in the background.

A pan-seared salmon fillet with crispy skin, topped with bright red roe and mushrooms. The fish rests on a bed of braised cabbage and cauliflower in a light broth on a white plate. The salmon is perfectly cooked with moist pink flesh contrasting with the golden-brown exterior.

The Thompson Problem.
https://www.youtube.com/watch?v=dNTnk1VFoJY
#GolfBalls #polyhedra #Goldberg
#maths #mathematics #geometry #electrons

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

#MathArt #geometry #animation #loop #geogebra #icosahedron #dodecahedron #polyhedra #3d

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

Made a buckyball. #truncatedIcosahedron #polyhedra #magnets

The first half of the buckyball: six pentagons made of golden spheres, and ten hexagons made of silvery ones, arranged in something like a hemisphere.

One more layer: fifteen hexagons now, giving a more pentagonal appearance.

Another five golden pentagons mean the form is only six polygons away from completion.

The complete truncated icosahedron - the same shape as a traditional football, or a C60 molecule, but made of spherical magnets. It is pictured here in the palm of my hand.

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

We now have a pentagonal section of a dodecahedron with a sphere as its face. This can be propagated back to a full sphere with a combination of circular patterns on 3 and mirrors, your call. (1-4)

In onshape at least, you can union the whole thing back into a sphere without error since we've defined the faces NOT (believe me, I tried this way first) as fractional degree angle to angle measures but with stepwise precise operations.

I figured since I spent most of my morning figuring this out, I'd share the process with other folks and hopefully keep it somewhat software agnostic.

<3

#cad #onshape #design #polyhedra

[5/5, end]

Perform an intersect boolean on both the revolves. this leaves a airfoil/kayak shaped piece, the edge away from the origin is one of the true edges of the (not yet spherical) dodecahedron. (1)

Create a three point construction plane on two vertices from the wedge and one vertex of the cube. This plane defines your first face. (2)

Draw a pentagon on that plane and stick it to the same points you used to create the plane. (3)

Create another plane on three points, this time for the two points of the wedge and the origin. This defines a midplane between two of the pentagonal faces. (4)

#CAD #onshape #polyhedra

[2/5]

HOW TO: Projecting an accurate (i.e. no chance for floating point errors to stack up and ruin your day) dodecahedron onto a sphere in CAD. This is possible because a cube shares some vertices with a dodecahedron as explained in https://www.archive.bridgesmathart.org/2009/bridges2009-123.pdf, img 1).

[NOTE: this took me 10x as long to figure out this process as I initially expected. The face to face angle way using arctan & fractional degree angles is -profoundly- cursed. There be dragons.]

Extrude a cube around the origin. (2)

On one square face, draw two pentagons so that the opposite edges of the square face match up with the longest vertices across a pentagon with the bulk of the pentagon sticking out into space. (3)

Separately, revolve (as "NEW" bodies) two of the larger trapezoidal sides of the pentagons on opposite sides of the square (4)

[1/5]

#cad #onshape #polyhedra

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

Each polygonal face has a complimentary polygonal hole. Each vertex is made from colourful folded paper, in an approximately hexagonal shape, folded in, so that the faces are concave.

https://en.wikipedia.org/wiki/Elongated_square_pyramid bestaat er een 4d-versie met Kubuspiramide en tesseract?
#wiskunde
#math
#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

Truncated icosahedron constructed from a regular icosahedron with the vertices cut off a third of the way along each edge. The ensuing polyhedron has 20 regular hexagon and 12 regular pentagon faces, 60 vertices and 90 edges and is similar to the pentagonal and hegagonal pattern on which old designs of football were based. The shape is also similar to the carbon-60 molecule or buckyball.

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

Rhombicuboctahedron coloured violet, displaying grid lines and axes and set against a black background. The polyhedron is made up of 8 equilateral triangle and 18 square faces.

ADEPTAPRIL/DEC04

Mistigram: If you have any Dungeons & Dragons players in your family you already know what you’re stuffing their stockings with: colourful platonic solids! This #ANSIart screen was drawn for National Dice Day by AdeptApril.

#4December #AdeptApril #ANSIArt #Dec4 #dice #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

#polyhedra #spacefilling #combinatorics

#polyhedra

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