From Newsgroup: sci.math


Hi!

recently I've been working on the Platonic, Archimedean and Catalan
solids in desmos (takes a while to load):

https://www.desmos.com/3d/jtgknkqldk?translucentSurfaces=1

What would be the most intuitive way to visualize the duality between
such solids?

I've found some images online that combine associated dual solids such
that every edge of one solid intersects exactly at a single point with
every edge of the associated dual solid.

https://i.imgur.com/NMWItAA.jpeg

https://i.imgur.com/D6X33Yc.jpeg

Is this the most intuitive way to visualize the duality relationship
between associated solids?

Some rough sketches of how to visualize the examples in those images in desmos:

https://www.desmos.com/3d/nkv3hhlr0e

https://www.desmos.com/3d/xqzxuzy0gf
--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: sci.math

On 02/01/2026 07:33 PM, sobriquet wrote:

Hi!

recently I've been working on the Platonic, Archimedean and Catalan
solids in desmos (takes a while to load):

https://www.desmos.com/3d/jtgknkqldk?translucentSurfaces=1

What would be the most intuitive way to visualize the duality between
such solids?

I've found some images online that combine associated dual solids such
that every edge of one solid intersects exactly at a single point with
every edge of the associated dual solid.

https://i.imgur.com/NMWItAA.jpeg

https://i.imgur.com/D6X33Yc.jpeg

Is this the most intuitive way to visualize the duality relationship
between associated solids?

Some rough sketches of how to visualize the examples in those images in desmos:

https://www.desmos.com/3d/nkv3hhlr0e

https://www.desmos.com/3d/xqzxuzy0gf

You might like Graustein's "Higher Geometry".

The notions of "duals" and "complementary duals",
like "point" and "space", and for things like
inner and outer or interior and exterior products
in the forms, make for a great account of completions.


--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: sci.math

Op 2-2-2026 om 06:49 schreef Ross Finlayson:

On 02/01/2026 07:33 PM, sobriquet wrote:

Hi!

recently I've been working on the Platonic, Archimedean and Catalan
solids in desmos (takes a while to load):

https://www.desmos.com/3d/jtgknkqldk?translucentSurfaces=1

What would be the most intuitive way to visualize the duality between
such solids?

I've found some images online that combine associated dual solids such
that every edge of one solid intersects exactly at a single point with
every edge of the associated dual solid.

https://i.imgur.com/NMWItAA.jpeg

https://i.imgur.com/D6X33Yc.jpeg

Is this the most intuitive way to visualize the duality relationship
between associated solids?

Some rough sketches of how to visualize the examples in those images in
desmos:

https://www.desmos.com/3d/nkv3hhlr0e

https://www.desmos.com/3d/xqzxuzy0gf

You might like Graustein's "Higher Geometry".

The notions of "duals" and "complementary duals",
like "point" and "space", and for things like
inner and outer or interior and exterior products
in the forms, make for a great account of completions.

Yeah, Grassmann and Clifford algebras are very interesting.. I've
been exploring various videos about them for some time now:

https://www.youtube.com/watch?v=2hBWCCAiCzQ&list=PLVuwZXwFua-0Ks3rRS4tIkswgUmDLqqRy

https://www.youtube.com/watch?v=qJHFTMF_pPk&list=PLffJUy1BnWj3deu0cqpk5CiePiwORDiCe

https://www.youtube.com/watch?v=9oCJO4Kmmj8

https://www.youtube.com/watch?v=nktgFWLy32U

--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: sci.math

Op 2-2-2026 om 04:33 schreef sobriquet:

Hi!

recently I've been working on the Platonic, Archimedean and Catalan
solids in desmos (takes a while to load):

https://www.desmos.com/3d/jtgknkqldk?translucentSurfaces=1

What would be the most intuitive way to visualize the duality between
such solids?

I've found some images online that combine associated dual solids such
that every edge of one solid intersects exactly at a single point with
every edge of the associated dual solid.

https://i.imgur.com/NMWItAA.jpeg

https://i.imgur.com/D6X33Yc.jpeg

Is this the most intuitive way to visualize the duality relationship
between associated solids?

Some rough sketches of how to visualize the examples in those images in desmos:

https://www.desmos.com/3d/nkv3hhlr0e

https://www.desmos.com/3d/xqzxuzy0gf

I guess a more natural way to visualize the duality is to show that each
of a pair of dual solids can be inscribed in the other, where vertices
and faces are interchanged:

https://www.desmos.com/3d/gib4szf2rd?translucentSurfaces=1
--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: sci.math

Op 6-2-2026 om 22:20 schreef sobriquet:

Op 2-2-2026 om 04:33 schreef sobriquet:

Hi!

recently I've been working on the Platonic, Archimedean and Catalan
solids in desmos (takes a while to load):

https://www.desmos.com/3d/jtgknkqldk?translucentSurfaces=1

What would be the most intuitive way to visualize the duality between
such solids?

I've found some images online that combine associated dual solids such
that every edge of one solid intersects exactly at a single point with
every edge of the associated dual solid.

https://i.imgur.com/NMWItAA.jpeg

https://i.imgur.com/D6X33Yc.jpeg

Is this the most intuitive way to visualize the duality relationship
between associated solids?

Some rough sketches of how to visualize the examples in those images
in desmos:

https://www.desmos.com/3d/nkv3hhlr0e

https://www.desmos.com/3d/xqzxuzy0gf

I guess a more natural way to visualize the duality is to show that each
of a pair of dual solids can be inscribed in the other, where vertices
and faces are interchanged:

https://www.desmos.com/3d/gib4szf2rd?translucentSurfaces=1

There was also a cool entry to the desmos math contest this year
that featured a neat way to generate the Archimedian solids in a more systematic fashion.

I've slightly tweaked it to show the Platonic and Archimedian solids consecutively.

https://www.desmos.com/3d/rsbzywfeia?translucentSurfaces=1

--- Synchronet 3.21b-Linux NewsLink 1.2