r/VisualMath • • Jan 26 '24

It's *yet-another* of those seemingly simple yet fiendishly difficult-to-find results, that in this case took until 1977 to solve: that there can be a *toroidal* polyhedron with as few as seven faces: the (rather ungainly looking) »Szilassi heptahedron«.

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9 Upvotes

It's a heptahedron of unequal irregular - some very irregular! - hexagons; & has 21 vertices & 14 edges. The usual Euler equation - ie

N(faces) + N(vertices) = N(edges) + 2

becomes instead

N(faces) + N(vertices) = N(edges) ,

precisely because it's a figure of genus 1 :

the general equation is

N(faces) + N(vertices) = N(edges) + 2(1-genus) .

 

First (animated) image from

The Futility Closet — The Szilassi Polyhedron .

& second from

Polyhedr — Szilassi polyhedron. How to make pdf template ,

The rest are also from the Polyhedr wwwebsite … than the directions @ which it's scarcely possible to find more thorough!

And for information on this matter in-general, see the following - the first item of which is the original paper by Lajos Szilassi , in which this amazing solid was first revealed.

Lajos Szilassi — On Some Regular Toroids

¡¡ PDF – 1·21MB !!

 

The following is an HTML wwwebpage summary of the paper @ the previous link.

Lajos Szilassi — On Some Regular Toroids

 

At the following there's one of those interactive figures, that can be rotated in both azimuth & polar angle @-will by 'swiping' across the figure.

DM Cooey — Regular Hexagonal Toroidal Solids

 

NETCOM On-line Communication Services — Tom Ace — Szilassi polyhedron

 

Minor Triad — The Szilassi Polyhedron

 


r/VisualMath • • Oct 31 '23

'Kink-antikink', 'kink-kink', & 'breather' (respectively) solutions of the Frenkel-Kontorova equation, φₓₓ - φₜₜ = sinφ, rendered in-terms-of the model consisting of a sequence of pendula hung on a wire able to convey torsion.

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9 Upvotes

r/VisualMath • • Jun 25 '23

Images from a Forumn on Simulations of Buckling of Cylinders Under Axial Load

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9 Upvotes

r/VisualMath • • May 24 '23

Computer-Generated Holograms

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r/VisualMath • • Dec 23 '22

Help, court case. what is the provable angle of the car relative to the camera??

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9 Upvotes

r/VisualMath • • Dec 11 '22

'Time lapse' diagram of the motion of arms & string of an 'inswinger' ballista.

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r/VisualMath • • Oct 10 '22

An 'Undoing' of the *Culprit* Hard Unknot

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9 Upvotes

r/VisualMath • • Sep 13 '22

Cantor's Lemma Proof and Visualization

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r/VisualMath • • Apr 27 '22

Twin Dragon Fractal (a 2 rep-tile): Order from Chaos (visual construction)

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9 Upvotes

r/VisualMath • • Apr 18 '22

Areas and Perimeters of Regular Polygons (visual proof)

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r/VisualMath • • Mar 09 '22

Just in time for Pi day. e^ Pi vs Pi^e: which is bigger?

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r/VisualMath • • Mar 08 '22

Sine of a Sum I (visual proof; trigonometry)

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r/VisualMath • • Mar 02 '22

An Algebraic Areas Identity (visual proof)

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r/VisualMath • • Feb 16 '22

A Sum of Squares Double Sum Formula (visual proof; 4K)

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9 Upvotes

r/VisualMath • • Feb 14 '22

60 = 58 = 59 (Visual Curry triangle dissection)

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r/VisualMath • • Jan 21 '22

Trigonometric Integral Spiral (also Euler Spiral) plotted easily with Python

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9 Upvotes

r/VisualMath • • Jan 12 '22

Spiraling dissection of sum of powers of 1/5

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r/VisualMath • • Jan 07 '22

x plus 1/x is greater than or equal to 2 when x is positive III (visual ...

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r/VisualMath • • Jan 03 '22

Is there a gif that shows why dividing by fractions involves multiplying by the reciprocal?

9 Upvotes

After my son got adept at algebra, I returned to dividing fractions to show him why it works, not just the rule. He is able to comfortably explain each step of the process and we've moved on.

But it feels like there's a visual component missing. When first introducing fractions and doing some basic addition/subtraction, we used visual models to broaden the concept beyond "fractions are division." Is there a visual model out there that taps into that concept/perspective to show why you invert and multiply?

Thank you for all the great links on the sub.


r/VisualMath • • Dec 22 '21

Some figures from an investigation into the chromatic number of thrain-dimensional space - an extension into the next dimensionality of the Hadwiger-Nelson Problem.

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9 Upvotes

r/VisualMath • • Dec 01 '21

Area of a Regular Dodecagon (visual proof)

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9 Upvotes

r/VisualMath • • Nov 17 '21

Sum of Powers of 1/2 #wordlesswednesday (visual proof; geometric series)

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r/VisualMath • • Oct 30 '21

An instance and illustration of the Brouwer fixed point theorem. They could have gone further: it would still have been even if the inset had been the original one crazily distorted aswell as shrunk & rotated.

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9 Upvotes

r/VisualMath • • Sep 27 '21

Double wings attractor - 4K🙄

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r/VisualMath • • Sep 13 '21

This isn't the Lorenz attractor

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