#polytopes

[knotty-et-al]

Polytope info card of the Truncated Cuboctahedron

Today I finished this friend-shaped archimedian solid.

I drew the tiny drawing in the down right corner of the card and resized it with my printer.

The drawing:

I drew this Truncated cuboctahedron in an isometric projection and used my beloved isometric dot paper.

To start with the truncated cuboctahedron I started to draw a cube (with pencil).

Then I altered the cube by drawing a cuboctahedron in it (with pencil as well). I truncated th vertices of the cube like in the depiction below:

Then I altered the cuboctahedron drawing with another truncation - resulting in the truncated cuboctahedron shape.

[For clarification: I later erased the pencil lines of the cube and cuboctahedron, because it became messy and these lines were just there to help in the drawing process.

For the photo I laid pictures of a cube and cuboctahedron besides the truncated cuboctahedron drawing to show the similarity between these shapes - and present the principle of truncation visually.)

#polytopes #polytope #polyhedra #polyhedron #cuboctahedron #truncated cuboctahedron #archimedian solid #archimedian solids #geometry #math #mathy stuffy #knottys math #polytope info cards #math art #mathy #mathematics

[cant-think-of-a-good-one]

thinkin about pentagonal rotunda

pe- pero

#mathblr #mathematics #geometry #polytopes #polyhedrons #polyhedra #polytopy #shapes #rotund

[best-shapes]

Taking submissions for your favorite shape! This will probably be the bracket after the next one, and I don't have the next one planned yet, so you have time to get your submissions in.

#Mathematics #Math #Geometry #Topology #Polytopes #Tumblr Polls #Tumblr Bracket #shapes

[more-mathematics-mor-lam]

It turns out that what we want from a hyperplane are the exact same things we want from a bra

#mathblr #polytopes #a breast is a kind of convex set

[wanderingandfound]

The pseudo rhombicuboctahedron and the pseudo great rhombicuboctahedron are so funny. False shapes. Pretender shapes. Nearly uniform, but with a slight twist that messes up one symmetry slightly. And their duals also have the same deal! They're the pseudo deltoidal icositetrahedron and the pseudo great deltoidal icositetrahedron!

#They're also called the elongated [cross] square gyrobicupola so like... they do have their own names. #But hey they're in an exclusive group of two! So congrats to the psuedouniform polyhedra for that! #I got lost in the sauce making this post. #The sauce being Wikipedia. #personal #polyhedra #polytopes #geometry #mathematics

[bysance]

Los Alamos, Art and Science exhibit.

July 8 – August 1st

View On WordPress

#Coxeter #geometry #mathart #polytopes #scienceandart

[tokinanpa]

I love reading stuff on abstract geometry because there'll be some extremely complicated construction of abstract polytopes that takes up like two full pages

and the first example is this

and you're like "wow that's a cube :)"

and then the next example is this

#thats the rectified 4_21 polytope btw #its 8-dimensional #math #mathematics #geometry #tokinanpa

[tanadrin]

feels like there's a rich vein of unexplored woo you could attach to stellation of polyhedra, as, like, a vehicle for the expression of mystical processes. i'm surprised it's something the ancient greeks didn't invent. they liked to overload geometry with weird metaphysical shit. and the way unassuming solid shapes turn into these visually complex, lacy, crystalline forms when you apply a pretty simple mathematical process is redolent of... something. i don't know what.

#like the pentagram is the most basic and boring stellation there is #you can do so much better! #make the symbol of the devil the last of the 7071672 enantiomorphous stellations of the icosidodecahedron! #make it a complicated stellation of a higher dimensional polytope no sane mind can percieve!

[brainwave-designs]

#sexy content #ai image #ai generated #ai art #ai #ai artwork #ai girl #ai illustration #desire #pinup #adobe photoshop #fooocus #polytope

[noosphe-re]

Tribe - A continuous set of semi-uniform polytopes (or compounds) that span several teepees. Truncation rotation is an example with one variable of morphing. Wythoffian cases will include all polytopes with a particular symbol (example xy^z) allowing the variables (x,y,z, etc) to take on any value including negative. The following pic displays the grid tribe (which contains 4 clans and 60 teepees). Each teepee is displayed twice on the pic with an example polyhedron within a triangle shaped region (the sides of the dual of grid). The grid tribe's clans are xy^z (grid), x,y^z (reboga), xy^'z (badori), and x,y^'z (robisu) - where x,y,and z take on positive values. There are 11 spitsu tribes under grid, they are xy^z (grid, 60 teepees), x*y^z (quitdid, 60 teepees), xy*z (gaquatid, 60 teepees), (x^y*'z) (idtid, 60 teepees), (xy*z) (becada, 30 teepees), (x^y^z,) (fabeca, 30 teepees), (xy^'z) (cafeta, 30 teepees), (x*y*z,) (mocaba, 30 teepees), (x^'y^'z^') (jefari, 10 teepees), (x*y*z*) (vamesa, 10 teepees), and the 15-block compound tribe x y z (broza, 5 teepees). I suspect that four dimensional tribes, such as the gidpixhi tribe could have as many as 7200 teepees with three variables of morphing. (source)

#geometry #polytope #science #dimension #math #mathematics

[knotty-et-al]

New challenge (to establish a daily routine): Creating one new polytope info card after breakfast - each day.

(That is the first page of the list of the polytopes I want to make. (92 Johnson solids will be very very much, and I have to stop myself from thinking about those many solids. but eeeh. we might approach it step by step... )

So, I started the polytope cards project some time in the summer of this year.

I already made all 5 platonic solids,

some regular 4-polytopes (the 4D platonic solids plus the 24-cell that has no 3D sibling),

and the first 4 archimedian solids.

Today I created the truncated octahedron card:

Yesterday I made the truncated tetrahedron card:

- - -- ---

The general template of the cards is as following:

This project is still in progress.

Furtherly I want to add:

General explanations/index cards/summaries

#mathy stuffy #geometry #math #polytope #polytopes #polytope info cards #shapes #polyhedra #polyhedron #archimedian solids #platonic solids #mathematics #math joy #math passion #mathy #knottys math #knottys mathy stuffy #wip #info cards #autism activities of joy #information collecting #pretty shapes #what is better than pretty shapes? collecting all sorts of infos and pictures about pretty shapes!

[cant-think-of-a-good-one]

hehe get spun

HUHH WUHH GUUUUHHH ?!??!! this is so cool !!!

wow thank you. somebody put work into making a thing on a website of me?? this is technically the first ever fanart of my polyhedron fursona thingy and i havent even made a ref sheet or anything. again thank you so much this means a lot :]]

they roate !! how did you make a 3d svg?? is that a thing now?

#fanart #calico #3d #3d art #cats #polytopes #truncated octatheydron

[best-shapes]

Regular-ish Convex Polyhedra (with bonus sphere) Bracket

The bracket has been seeded!

Round 1:

Sphere vs Rhombicosidodecahedron

Truncated Octahedron vs Snub Cube

Icosidodecahedron vs Truncated Cube

Cuboctahedron vs Tetrahedron

Cube vs Rhombicuboctahedron

Truncated Dodecahedron vs Snub Dodecahedron

Truncated Icosahedron vs Truncated Icosidodecahedron

Dodecahedron vs Truncated Cuboctahedron

Tetrahedron vs Deltoidal Hexecontahedron

Tetrakis Hexahedron vs Pentagonal Icositetrahedron

Rhombic Triacontahedron vs Triakis Octahedron

Rhombic Dodecahedron vs Triakis Tetrahedron

Octahedron vs Deltoidal Icositetrahedron

Triakis Icosahedron vs Pentagonal Hexecontahedron

Pentakis Dodecahedron vs Disdyakis Triacontahedron

Icosahedron vs Disdyakis Dodecahedron

#Tumblr Bracket #Tumblr Tournament #shapes #geometry #polyhedra #polytopes #Platonic Solids #Archimedean Solids #Catalan Solids #Round 1

[more-mathematics-mor-lam]

Good morning to arrangements of hyperplanes and arrangements of hyperplanes alone 🌀

#polytopes #mathblr

[python-programming-language]

Auf in die Welt der vierten Dimension ...

Der Sprung von der Fläche zur Ebene ist auch für Laien nachvollziehbar. Aber Mathematiker*innen wagen sich gerne weiter vor: Alicia Boole widmete ihr Leben der Suche nach regelmäßigen Körpern in der 4. Dimension - und sie wurde fündig, obwohl ihr als Frau zeitlebens eine universitäre Ausbildung verwehrt blieb. Auf ins Land der Polytope!

Post #116: YouTube, Arte, Mathewelten, Die vierte Dimension, 2024.

#arte #mathewelten #dimension #vierte dimension #polygone #polytope #alicia boole #Youtube #geometrie #geometry #maths

[bysance]

Los Alamos, Science and Art exhibit

July 8 – August 1, 2023

View On WordPress

#losalamos #mathematicsandart #polytopes #scienceandart