#Hypercube

[13thpythagoras]

Tesseract - Hypercube 4th dimension Infinity Mirror Art Sculpture by Nic...

[daily-public-domain]

Day 53: Views of the Tesseract

link

--This image is part of the public domain, meaning you can do anything you want with it ! (you could even sell it as a shirt, poster or whatever)--

[epitome-the-burnkid-viii]

[ketrinadrawsalot]

The Octochoron answers to many names--Tesseract, Hypercube, 8-Cell, and Free Hugs. She will happily receive hugs as well as give them.

[jacobjoaquin]

Liminal Tesseract

[ne0nwithazero]

Thinking about hypercube again

[catheadreynolds]

Poem

[art-of-mathematics]

The task I wanted to do:

- task 1: Visualize the fourth dedekind number

What I needed to do in order to do task 1:

- task 1.1: Draw a hypercube and

- task 1.2: then give each of the 16 vertices a name - which is the 16 different "cells" (I dunno which word to use, sorry) of a venn diagram with 4 overlapping sets plus a circle around that 4-venn diagram.

- - -- ---

//additional info: For the 3rd dedekind number visualization I already posted I needed to use 20 cubes. Each of the 8 vertices of a cube was related to 3 sets - A, B and C - and the intersections of these sets. (AB, AC, BC, ABC)

You remember this post:

... and these details:

...and now back to the 4th dedekind number, which follows the same principle, - but in 4 dimensions.

- So we need a hypercube - and a 4th set/letter:

Now we have 4 letters - alias 4 sets

- and 11 combinations of these sets:

AB, AC, AD, BC, BD, CD, (6)

ABC, ABD, ACD, BCD, (4)

ABCD (1)

=> 11 different intersections + 4 "pure" sets. (sorry for ignorant wording)

So, we have 15 of these now. What is with the 16th (as the hypercube has 16 vertices)? Yeah, that one is the circle you imagine around the 4-set venn diagram.

- - -- ---

This is a 4-set venn diagramm btw:

--- -- - -

So, back to me attempting to do the 4th dedekind-number visualization:

So I started to draw that venn diagram using ellipses, but I slightly altered it, because I wanted to use my isometric grid paper. (The angles of my drawing are different than in the picture depicted above.)

I started to draw the 4 ellipses, and I somehow started to see two intertwined/interlocked tubes due to the additional helplines I used for drawing.

Then I started to use my thicker black pen to make this effect of these two interlocked tubes more visible:

Now I plan to write the sets/letters at the backside of that piece of paper - in mirrored, so I can hold this piece of paper (with the tube drawing in front) against the light - and see the letters of the set names shining through.

i might also add some details to the tubes.

[klovercrown]

The look I give when someone says they like Hypercube more than Cube

[rjalker]

I'm sure I could keep going but I'm too lazy to change the canvas size for all of them since I wanted them all to be the same size. not perfect but good enough.

[ID: Six simple geometric drawings, showing the progression from a single point, to a straight line, to a rectangle, to a 3D rectangle, to a 4D rectangle, an finally, attempt at a 5D rectangle. Each progressive shape is made by copying and pasting the one before it, and moving it, then connecting the two with more lines, making a more and more intricate shape representation. The point is a single black dot on the Left side of the screen. The line is two horizontal dots joined by a line between them. The rectangle is the line pasted again below the first, joined by two vertical lines. The 3D rectangle, or cuboid, is the rectangle copy and pasted on a diagonal, with four more diagonal lines connecting the original with the clone. The 4D rectangle, or hyperrectangle, has the copy of the cuboid dragged slightly down and to the side, with six new lines connecting them. The 5D rectangle has a copy of the hyperrectangle pasted again on a diagonal, with eight new lines connecting the two.

these are public domain because I said so. use for whatever you want.

[theothin]

What is your MTG project?

it's what I've been calling a hypercube - a group of mini-cubes that can be combined in various configurations. the main type of mini-cubes I've been aiming for are 90 cards and focused on a single set, ideally including cards suitable for a set jumpstart cube, since set jumpstart cubes are great ways to set up quick games. being focused on a single set also means that after combining the cards together for a larger cube, it's easy to separate them and determine which mini-cube they belong to. for sets where I don't have as many cards, I've been going for smaller batches of 15, 30, or 45, and in some cases combining cards from multiple related sets

once it's complete, I plan to post it along with a more extensive writeup, but there's still some things I want to sort out in the meantime. so far, I've picked about 8,000 cards to include, and over the past couple of days I've started sleeving some of the mini-cubes, which is of course quite an undertaking!

[geneticallymodifiedshitposts]

i'm not like other girls. i'm a 5-dimensional hypercube

[orpheusterminals]

[ne0nwithazero]

The hypercube is gender to me, i dont know how else to explain it

It just makes sense, I feel both so abstract but also like 3 dimensions aren't enough!!!

It does feel like i'm often floating out there, comprehension just out of reach, I can understand myself in theory, but to witness myself in my entirety? Perhaps it would drive me insane

[axiomaticsystem]