#icosohedrons

[thefrostychemist]

Do you ever wonder if someday d20s will be used as a divining instrument? Like the practice of rolling a d20 for success or failure is already so widespread, and it's already used ironically to refer to real life scenarios, so we can absolutely see it making the leap to superstition and eventually even to a standard means of divination, complete with symbolism and interpretation.

[paradoxlemonade]

what fic/au were you working on most recently, what is it about, and how did you come up with it?

Hi Rose!!! Omg okay so. I have transed so many genders. Because I am trans and it's fun lol

I've been on a bit of a hiatus from fic writing up until very recently, but a few weeks ago I pulled a year-old concept out of the depths of my Google drive and now it once again has a chokehold on me </3

The background is this: Ysione (Evil Xisuma) was sent off of Hermitcraft to make friends because the only people they ever talked to willingly were Xisuma and Zedaph. While out, they discover a fun server plugin that swaps the sex of whomever it affects and is mainly used for... Private servers of a certain persuasion. They decide that it would be a fun prank to send to their brother unannounced.

...Except that when the worm he made drops its payload, it spreads and affects everyone on hermitcraft and resists attempts to remove it.

Oops...?

That all happens off page.

On page are the rest of the hermits in various stages of glee and/or severe distress. The hermits that already knew they were trans (i.e., Grian, Gem) are having a great time. Cis hermits range from using the plugin for its intended purposes (Keralis and xB lmao), to vague but manageable discomfort (False, Impulse), to suffering (Doc and Etho), to having a gender crisis (Tango). I have a whole spreadsheet to keep track of how different hermits have reacted to the plugin :D If anyone is curious about how a particular hermit reacted I can and will infodump at a moment's notice.

The story is all about friendship, community, body image, gender identity, and mutual support. Even when they're Going Through It, I wanted the overall impression of the story to be gentle and feel-good.

[dyst-blogs]

I like words that make writing haikus easier. icosohedron

[theshitpostcalligrapher]

what, you got beef with my boy the icosohedron?

not the icosohedron.....

[dyst-pics]

magical icosohedron

[drink-the-stars]

Stellated Dodecahedron and icosohedron respectively

[kusudamalab]

"Memory Cell" Organic Sculpture. Size: 5x5x5 in / 12x12x12 cm. Material: Special treated fiber. Ready to find a new owner. . #sacredgeometry #sculpture #healingenergy #healingvibrations #platonicsolids #dodecahedron #icosohedrons #icosahedron #organic https://www.instagram.com/p/BxlNA_nBnWX/?igshid=1pdc3tllu2xkj

[earthstory]

Holy moly now this is quartz.

gemcutter3

Not For Sale!

One of my favorite things I've cut in the past few years. A 16.85ct Ametrine Icosohedron or D20 dice typically used for role playing games like Dungeons & Dragons. I plan on cutting some more of these but they will typically be pretty small compared to a standard die and won't have numbers on them.

[object-tournament]

reasons to vote rhombicosidodecahedron:

one of the largest archimedian solids!

vertex-transitive, so each point where 4 faces meet is identical to the rest!

the cantellation of a dodceahedron or an icosohedron, depending on how u look at it

the best 3D shape (im biased)

reasons to vote butter:

useful ingredience!!

square prism, very shaped

good on a bagel

slipperey

tot2023: wave 5

round 3, match 56

[id: two pictures. the first shows a green render of a rhombicosidodceahedron, a polyhedra with triangular, square and pentagonal faces, the second 3 sticks of butter. end id.]

[mindhuestudio]

Hoping to start playing with the world tesselation project that's been kicking around for a few months now... First, however, it's good to make sure which triangles border which other triangles. . #worldtesselation #icosohedron #mapprojection #numbering #measuretwicecutonce #1234567891011121314151617181920 https://www.instagram.com/p/CMX-vbjFs0g/?igshid=moeumbhq32ay

[reflexletterpress]

Trying to get back to the @mindhue world tesselation project... First, we need to make sure we know which triangle borders which other triangle. . #letterpress #bostonprinter #printing #bostonpress #crankclickyankback #type #lead #tin #antimony #vandercook #stovefactory #Charlestown #ink #paper #inkonpaper #worldtesselation #icosohedron #mapprojection #numbering #measuretwicecutonce #1234567891011121314151617181920 https://www.instagram.com/p/CMX-jNKhocx/?igshid=1aked3xh3vrld

[abnormoinfo]

Dorbo Abodal #26, this one is about staying hydrated

[ patreon ]

[somethingusefulfromflorida]

Mattel should make different versions of the Magic 8 Ball that have different answers in different proportions. The standard 8 Ball uses an icosohedron, a 20-sided die, with answers printed on the faces; 10 are affirmative, 5 are non-committal, and 5 are negative. They should make a Tragic 8 Ball that has more No's then Yes's, or a DND tie-in that uses a regular d20 with numbers on it so you can "roll" it for your campaign, or platonic solids with different numbers of faces like a dodecahedron (12) or an octahedron (8). They could make a Lucky 7 Ball or an Unlucky 13 Ball, a Magic Cue that gives fortune cookie fortunes instead of yes-or-no answers, a whole set of 16 Magic Pool Balls that could be the exact same as the 8 just with different skins like collector's items (if the company really wanted to be insidious, they could sell them in blind boxes so you would have to buy dozens to find all 16)

I think a Magic Chalk Cube would be hilarious.

There are so many options; Mattell, hire me!

[bixbiboom]

[ID: A photo of Q and her husband Sam. They’re lying together on a couch, side by side, and both wearing the same shirt featuring the D&D logo inside a rainbow-colored outline of an icosohedron. Text at the bottom of the image reads “At least we’re twinning.” /end ID]

[432oneness]

Just made this set of Pyramids for the Sacral Chakra

432oneness.etsy.com 

[kitwallace]

Slicing up polyhedra with Hamilton

My explorations of Hamiltonian circuits on the face of a cube and other polyhedra continues.

A Hamiltonian circuit around the faces of a polyhedon touches each face once and once only and returns to the start.  Normally we think of a circuit around the vertices of a polyhedron, but I’m interested in the path around the faces of a polyhedron, equivalent to a path around the vertices of its dual. 

I had managed to cut a tubular path on the surface of a polyhedron, given a sequence of faces in the circuit.  So the pressing problem was to be able to compute  Hamiltonian circuits for ‘any’ polyhedron.

Computing Hamilton circuits

It’s well-known that the computation of Hamiltonian circuits is NP-complete but there are clever ways to do it quite efficiently. I learnt from Bob Bosch’s book Opt Art about the Concord TSP (Travelling Salesman Problem) solver and I look forward to understanding how to express the Hamiltonian circuit problem  for solution as a TSP. 

However, for experimentation and  for small numbers of faces or rather small numbers of small faces,  an exhaustive search is feasible.  I designed my algorithm so that it could be restricted to adjacent edges  - that’s no restriction for triangular faces so the maximium size of the search space for a polyhedron with only trianges (like an icosahedron)  is 2^N  where N is the number of faces. I had hoped that the restriction to adjacent edege might find a quicker solution for the dodecahedron, but there were no such solutions.  For the dodecahedron with its pentagonal faces,  the maximum search space is 4^N  ie 2^2N = 2^24.  ie about 16 million.  (I’m sure lower bounds are known). I made no attempt to eliminate paths which are ‘the same’ because I’ve no idea how to do that. The computed circuits all start on face 0 so there are no cyclical duplicates.

In practice the search space is much smaller that that upper bound. The openSCAD algorithm finds 2048 circuits for a dodecahedron in about 5 minutes (Core I5 Thinkpad).

It’s useful to be able to visually check that a circuit is Hamiltonian.  For example one circuit has faces indexes [7, 10, 1, 3, 9, 4, 11, 6, 5, 2, 8, 0].  In openSCAD I can add the face indexes to the faces to check. The path is marked with a tube, square in cross-section. The path runs from edge-midpoint to edge-midpoint in a series of ‘arc’s  or straight lines if the edges are parallel : ‘arcs’ because if the edges dont have equal length, the arc radius is interpolated between the edges. The arcs always meet the edge at right-angles. Subtracting the tube from the polyhedron incises the circuit on the surface: [ view STL ]  

Cutting a ball-bearing track

My orginal aim had been to cut a tube around the path in which a ball bearing could run, as Bob had done with his hand-carved cube.  It looked difficult to print such objects well on my home printer, and to be able to get the ball into the track, so I turned my attention to cutting the polyhedron into printable pieces.

Cutting a  polyhedron

The Hamiltonian circuit cuts the surface of the polyhedron into two parts.  Thus we can cut the solid into two parts by constructing a parting surfaces which extends from the path on the surface of the polyhedron to the centre. 

This parting surface is itself quite interesting. This is the dodecahedron circuit above [View STL]

Separating the halves

I wondered how to separate the two halves - seems impossible in openSCAD but I discovered that it was trivial to separate the generated STL in Slic3r - you just load the STL and click Split to separate the two halves. This allows each half to be saved as STL and  printed. For some polyhedra and circuits,  the two halves are the same and two copies can be fitted together: 

 Tetrahedron:

Cube - 1  [View STL]

cube 2  [View STL]

Others interlock  and can’t be re-assembled - difficult to print too!: 

 Icosohedron

In other case, the two halves form a chiral pair - these are the two halves of  a truncated tetrahedron:

Some prints:  L to R , top to bottom: Cube style1, truncated tetrahedron (chiral),Cube Style 2, octahedron, pentagonal prism

Multiple cuts

To make the solid assemblable, we can use two or more cuts.  On a cube there are only 4 circuits composed only of arcs. Two of these cuts the cube into 2 pairs of parts:  [view STL]

The dodecahedral challenge

A single cut creates two inseparable pieces:

but multiple cuts would create a multi-part division where the pieces are more likely to be separable, and hence assemblable, perhaps in a constrained order. Two cuts of the dodecahedron still created large interlocked pieces, but three randomly selected circuits cut the shape into 13 separate and different pieces.  

It would be a challenge to print them all and not know until the end whether the dodecahedron can be assembled - it would be good to be able to compute the best selection of the circuits to achieve this - something for another day!

Assembly

The pieces don’t reassembly securely. One approach would be to hollow out a cavity and add magnets to the piece.  This cube has been split and a cylinder, whose direction is normal to the plane at the centre, removed to make space for a magnet in each half:

OpenSCAD

This project is a good demonstration of the power of this language.  As a functional language with vector operations, it's capable of computing the Hamiltonian circuits on a polyhedron defined by faces and vertices, and of computing a path of points along one of those circuits.  But it’s also able to handle the rendering of a polyhedron as a solid and, using the CSG operations, to union,hull,  and difference objects.  A very powerful combination, although sometimes difficult to know which paradigm to work with.

The code is on GitHub