#truncated dodecahedron

[knotty-et-al]

Truncated dodecahedron

By cutting off the vertices of the dodecahedron you get the truncated dodecahedron.

This results in the 12 pentagonal faces of the dodecahedron turning into 12 dekagonal (10-gonal) and 20 triangular faces.

(As the dodecahedron has 20 vertices, truncation results in 20 triangular faces.)

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 2

Propaganda

Cube:

Also called the Regular Hexahedron

Platonic Solid

Regular

Dual of the Regular Octahedron

It has 6 square faces, 12 edges, and 8 vertices.

Image Credit: Tumblr

Rhombicuboctahedron:

Also called the Small Rhombicuboctahedron

Archimedean Solid

Semiregular

Dual of the Deltoidal Icositetrahedron

It has 18 square faces, 8 regular triangular faces, 48 edges, and 24 vertices.

Image Credit: @anonymous-leemur

Cube and Rhombicuboctahedron Together

Oh, cmon! The cube is great! It tiles space, its one of the platonic solids that has analouges in all dimensionalities, its vertices are can be mapped to the strings of three binary digits in a structurepreserving way, and its literally the most iconic shape of all time!

What is the rhombicuboctahedron? it has cubical symmetries, its by far the least interesting archimedean solid, it has a bullshit rotated version that noone can decide is archimedean or not, and its much worse than the cube in every way. The fact its winning is damning the entire electorate of this poll as pretentious neophytes who have seriosly considered polyhedra as beautiful and interesting construct in their on right, and are just voting for the shiniest thing they havent seen before.

Truncated Dodecahedron:

Archimedean Solid

Semiregular

Dual of the Triakis Icosahedron

It has 12 regular decagonal faces, 20 regular triangular faces, 90 edges, and 60 vertices.

Image Credit: Cyp

[the-silly-words-on-your-screen]

hello there old friend

TRUNCATED DECACHORON

SPREAD THIS ALL OVER TUMBLR FOR NO REASON

[sozeugs]

[dailypolyhedra]

Polyhedron of the Day #213: Antitruncated great dodecahedron

The antitruncated great dodecahedron is a semi-uniform polyhedron. It has 24 faces (12 pentagrams, 12 pentapods), 90 edges, and 60 vertices. It is also known as the inflected truncated great dodecahedron. It is constructed by antitruncating the great dodecahedron or by faceting the small rhombicosidodecahedron. Its dual is the antiapiculated small stellated dodecahedron.

Image created using Robert Webb's Stella software, found at https://www.software3d.com/Stella.php.

[phaseshapes]

Iridescence Star, my other Truncated Great Stellated Dodecahedron. Or you could think of it as "parking lot oil rainbow star". This was a nice shape to make, but don't expect to see any more of them. It's been thoroughly replaced by cooler shapes that I'd rather make! Coming soon!

[pancakeke]

[real-british-empire]

STOP POSTING TRUNCATED DODECAHEDRON

No, it’s revenge :3

[art-of-mathematics]

Drawing a snub dodecahedron (in isometric perspective) is quite lot of work, because I have to start with a dodecahedron (easy), then make an isocidodecahedron out of it (quite a lot of work) , and then make a truncated icosidodecahedron out of it (very much work) and then, after all these steps I can make the snub dodecahedron from this.

It is a similar procedure I used for drawing the snub cube:

Started with cube, then cuboctahedron, then truncated cuboctahedron, then snub cube.

[robotblues]

A Space-Filling Pair of Polyhedra: The Cuboctahedron and the Octahedron There are only a few polyhedra which can fill space without leaving gaps, without “help” from a second polyhedron. This filling of space is the three-dimensional version of tessellating a plane. Among those that can do this are the cube, the truncated octahedron, and the rhombic dodecahedron. If multiple polyhedra are allowed in a space-filling pattern, this opens new possibilities. Here is one: the filling of space by cuboctahedra and octahedra. There are others, and they are likely to appear as future blog-posts here. Software credit: I made this virtual model using Stella 4d, polyhedral-manipulation software you can buy, or try as a free trial download, at http://www.software3d.com/Stella.php.

[knotty-et-al]

New polyhedron drawing just dropped:

Triakis Icosahedron [dual of the Truncated Dodecahedron]

In order to draw that triakis icosahedron I drew a truncated dodecahedron (picture of truncated dodecahedron attached above)

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 1

Propaganda

Truncated Dodecahedron:

Archimedean Solid

Semiregular

Dual of the Triakis Icosahedron

It has 12 regular decagonal faces, 20 regular triangular faces, 90 edges, and 60 vertices.

Image Credit: Cyp

Snub Dodecahedron:

Also called the Snub Icosidodecahedron

Archimedean Solid

Semiregular

Dual of the Pentagonal Hexecontahedron

It has 12 regular pentagonal faces, 80 regular triangular faces, 150 edges, and 60 vertices.

Chiral so it has two forms that are mirror images of each other.

With 92 faces it has the most of the Archimedean Solids.

Image Credit: Cyp

[k00294490]

Tuesday 21st November

I realised today that the shape I was thinking of wasn't made out of octagons at all. I was looking at a truncated octahedron but that wasn't quite it either.

After speaking with Mike Fox who showed me the platonic solids shapes, I chose a dodecahedron. It's made out of pentagons.

I struggled to draw it so I found a template to fold it and help me visualise it.

[dailypolyhedra]

Polyhedron of the Day #230: Antitruncated great stellated dodecahedron

The antitruncated great stellated dodecahedron is a semi-uniform polyhedron. It has 32 faces (12 propeller stellapods, 20 triangles), 90 edges, and 60 vertices. It is also known as the inflected truncated great stellated dodecahedron. It can be constructed by antitruncating the great stellated dodecahedron or as a faceting of the truncated dodecahedron. Its vertex figure is an isosceles triangle. Its dual is the antiapiculated great icosahedron.

Image created using Robert Webb's Stella software, found at https://www.software3d.com/Stella.php.

[phaseshapes]

The Uranium Urchin

When an icosahedron is covered in 36º pyramids, it's called a Great Stellated Dodecahedron. These pyramids have been truncated, making this a "Truncated Great Stellated Dodecahedron". The paint is "iridescent graphite" with sand gel. And neon green, as you can see in the blacklight video above. I printed this shape in 2022 and finished it in 2023.

[i-am-thedragon]

Dodecahedron and truncated icosidodecahedron

So first of all, it's interesting that you specified truncated icosidodecahedron and not great rhombicosidodecahedron. When doing a bit of research to answer this one I found that the latter is sometimes incorrectly referred to as the former. "incorrectly", because the truncation of an icosidodecahedron apparently produces rectangular faces where the great rhombicosidodecahedron has squares.

This has interesting social implications because while the truncated icosidodecahedron may appear to be an Archimedean solid at first glance, and may be accepted as one by some people, others may consider them to not be Archimedean. Their rectangular faces may be seen as a very mild irregularity, or they may simply be considered a zonohedron instead.

Whether or not the person in question is, geometrically, an Archimedean solid or not, the potential outcomes of their offspring with a dodecahedron remain mostly the same.

This pairing could produce a few different solids as offspring, consisting almost entirely of Archimedean solids, unless said offspring end up just being a dodecahedron like one of its parents.

The pentagonal faces of the dodecahedron and the hexagonal faces of the truncated icosidodecahedron could combine to form a truncated icosahedron (the 'soccer ball' shape). The pentagonal and square faces could also form a small rhombicosidodecahedron, also forming triangular faces that neither parent possesses (which is fairly normal in Spacelander genetics). A truncated dodecahedron could also be a potential offspring, inheriting dodecahedron genetics while also expressing the decagonal faces of the truncated icosidodecahedron. This one also has some triangular faces.

Other kinds of visually similar Archimedean solids could also potentially be produced depending on certain genetics carried over from the grandparents. If the truncated icosidodecahedron does in fact have rectangular faces and is not an Archimedean solid, the offspring could also carry a similar train and have zonogonal faces in place of regular polygons.