Tournaments for Shapes!

This blog will be for shape tournaments! First off: 32-entry bracket between the Platonic Solids, Archimedean Solids, Catalan Solids, and the Sphere. Round 2 started December 20th. Profile picture and mobile header from anonymous-leemur.

[best-shapes]

Congratulations to the winners of our first bracket! All images drawn by Kepler.

Regular Icosahedron

Truncated Icosidodecahedron

Rhombic Triacontahedron

I have an idea for our second bracket, but I haven't determined our final contestants let alone seeded the bracket, gathered images, or collected propaganda. So I don't know when Bracket 2 will be posted. It will be about two-dimensional shapes, and will hopefully have at least one non-convex participant.

In the meantime, submit your favorite shape for Bracket #3!

I can also be found at my podcast tournament blog, and I'm a co-mod at haveyouheardthispodcast.

[wickedsick]

Which Geometric Transformation is the Hottest?

Rotation

Translation

Uniform Scaling

Non-Uniform Scaling

Reflection

Shearing

Voting ended onMar 10

[bumpscosity]

[wanderingandfound]

New profile picture! The Tumblr-style truncated icosidodecahedra were made by @anonymous-leemur, and I recolored them using @arokill‘s recolor of Gilbert Baker’s nine-stripe Pride flag.

[bestfictionalplant]

Round 1, Group 8

Best Fictional Plant

Yatevon (OCTAHEDRON: Transfixed Edition)

Echo Flower (Undertale)

Voting ended onMar 5, 2024

Yatevon transcript

Yatevon Octahedron A single-minded univore from the land of Dodecas, with a curious hunger for floating platforms. Octahedron - 004 - (005) Limited Edition

Propaganda and spoilers under cut

Yatevon: It's only purpose is to be an annoying enemy that steals your platforms. It's described as a "simple minded univore with a curious hunger for floating platforms". Oh and it's named after Yateveos.

Echo Flower: The Echo Flower is a mysterious cyan flower that repeats back whatever words it heard last, over and over. In Undertale, you can use it to hear conversations of passersby.

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 5 (Third Place)

Which shape is better?

Snub Cube

Rhombic Triacontahedron

Voting ended onJan 19, 2024

Propaganda

Snub Cube:

Also called the Snub Cuboctahedron

Archimedean Solid

Semiregular

Dual of the Pentagonal Icositetrahedron

It has 6 square faces, 32 regular triangular faces, 60 edges, and 24 vertices.

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

Image Credit: Cyp

Rhombic Triacontahedron:

Also called the Triacontahedron

Catalan Solid

Dual of a quasiregular polyhedron

Dual of the Icosidodecahedron

It has 30 rhombic faces, 62 edges, and 32 vertices of two types.

One of the 9 edge-transitive convex polyhedra along with the 5 Platonic Solids, the 2 Quasiregular Convex Polyhedra, and the Rhombic Dodecahedron.

It has both the tumbling block quilt pattern and a five-pointed star on its surface.

Image Credit: Maxim Razin based on Cyp

[best-shapes]

With 60% of 135 votes, the Rhombic Triacontahedron wins third place in the Regular-ish Convex Polyhedra bracket!

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 5 (Finals)

Which shape is better?

Truncated Icosidodecahedron

Regular Icosahedron

Voting ended onJan 19, 2024

Propaganda

Truncated Icosidodecahedron:

Also called the Rhombitruncated Icosidodecahedron, Great Rhombicosidodecahedron, Omnitruncated Dodecahedron, Omnituncated Icosahedron

Archimedean Solid

Semiregular

Dual of the Disdyakis Triacontahedron

It has 12 regular decagonal faces, 20 regular hexagonal faces, 30 square faces, 180 edges, and 120 vertices.

It has the most edges and vertices of all platonic and archimedean solids.

Of the vertex-transitive polyhedra, it fills up the most of the volume of the sphere it fits in (89.80%).

It is not actually the shape you get when you truncate an icosidodecahedron, although it is topologically equivalent.

It is the mod's favorite three-dimensional shape.

They made a void truncated icosidodecahedron and it's glorious. I had one for a while, it's hard to turn because of alignment issues, especially the decagonal sides. Fun puzzle tho, never did figure out how to permute the last layer...

Image Credit: @anonymous-leemur

Regular Icosahedron:

Platonic Solid

Regular

Dual of the Regular Dodecahedron

It has 20 regular triangular faces, 30 edges, and 12 vertices.

Image Credit: @etirabys

[best-shapes]

With 57.5% of 454 votes, the Regular Icosahedron is crowned the winner of the Regular-ish Convex Polyhedra bracket!

I would like to thank anyone and everyone who voted for the Truncated Icosidodecahedron. I never expected my favorite shape would place second in this tournament, and the options as I see them are either scores of people agree with me that it's a good shape, or that people voted for it because I asked them to. Either way, thank you so very much. <3

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 5 (Third Place)

Which shape is better?

Snub Cube

Rhombic Triacontahedron

Voting ended onJan 19, 2024

Propaganda

Snub Cube:

Also called the Snub Cuboctahedron

Archimedean Solid

Semiregular

Dual of the Pentagonal Icositetrahedron

It has 6 square faces, 32 regular triangular faces, 60 edges, and 24 vertices.

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

Image Credit: Cyp

Rhombic Triacontahedron:

Also called the Triacontahedron

Catalan Solid

Dual of a quasiregular polyhedron

Dual of the Icosidodecahedron

It has 30 rhombic faces, 62 edges, and 32 vertices of two types.

One of the 9 edge-transitive convex polyhedra along with the 5 Platonic Solids, the 2 Quasiregular Convex Polyhedra, and the Rhombic Dodecahedron.

It has both the tumbling block quilt pattern and a five-pointed star on its surface.

Image Credit: Maxim Razin based on Cyp

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 5 (Finals)

Which shape is better?

Truncated Icosidodecahedron

Regular Icosahedron

Voting ended onJan 19, 2024

Propaganda

Truncated Icosidodecahedron:

Also called the Rhombitruncated Icosidodecahedron, Great Rhombicosidodecahedron, Omnitruncated Dodecahedron, Omnituncated Icosahedron

Archimedean Solid

Semiregular

Dual of the Disdyakis Triacontahedron

It has 12 regular decagonal faces, 20 regular hexagonal faces, 30 square faces, 180 edges, and 120 vertices.

It has the most edges and vertices of all platonic and archimedean solids.

Of the vertex-transitive polyhedra, it fills up the most of the volume of the sphere it fits in (89.80%).

It is not actually the shape you get when you truncate an icosidodecahedron, although it is topologically equivalent.

It is the mod's favorite three-dimensional shape.

They made a void truncated icosidodecahedron and it's glorious. I had one for a while, it's hard to turn because of alignment issues, especially the decagonal sides. Fun puzzle tho, never did figure out how to permute the last layer...

Image Credit: @anonymous-leemur

Regular Icosahedron:

Platonic Solid

Regular

Dual of the Regular Dodecahedron

It has 20 regular triangular faces, 30 edges, and 12 vertices.

Image Credit: @etirabys

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 5 (Third Place)

Which shape is better?

Snub Cube

Rhombic Triacontahedron

Voting ended onJan 19, 2024

Propaganda

Snub Cube:

Also called the Snub Cuboctahedron

Archimedean Solid

Semiregular

Dual of the Pentagonal Icositetrahedron

It has 6 square faces, 32 regular triangular faces, 60 edges, and 24 vertices.

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

Image Credit: Cyp

Rhombic Triacontahedron:

Also called the Triacontahedron

Catalan Solid

Dual of a quasiregular polyhedron

Dual of the Icosidodecahedron

It has 30 rhombic faces, 62 edges, and 32 vertices of two types.

One of the 9 edge-transitive convex polyhedra along with the 5 Platonic Solids, the 2 Quasiregular Convex Polyhedra, and the Rhombic Dodecahedron.

It has both the tumbling block quilt pattern and a five-pointed star on its surface.

Image Credit: Maxim Razin based on Cyp

[positivelyprime]

Please vote snub cube!! It is the best way to maximize the distance of 24 points on a sphere!!

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

WHOOO !!!

SNUB CLUB !!!

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 5 (Third Place)

Which shape is better?

Snub Cube

Rhombic Triacontahedron

Voting ended onJan 19, 2024

Propaganda

Snub Cube:

Also called the Snub Cuboctahedron

Archimedean Solid

Semiregular

Dual of the Pentagonal Icositetrahedron

It has 6 square faces, 32 regular triangular faces, 60 edges, and 24 vertices.

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

Image Credit: Cyp

Rhombic Triacontahedron:

Also called the Triacontahedron

Catalan Solid

Dual of a quasiregular polyhedron

Dual of the Icosidodecahedron

It has 30 rhombic faces, 62 edges, and 32 vertices of two types.

One of the 9 edge-transitive convex polyhedra along with the 5 Platonic Solids, the 2 Quasiregular Convex Polyhedra, and the Rhombic Dodecahedron.

It has both the tumbling block quilt pattern and a five-pointed star on its surface.

Image Credit: Maxim Razin based on Cyp

[positivelyprime]

Please vote snub cube!! It is the best way to maximize the distance of 24 points on a sphere!!

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 5 (Third Place)

Which shape is better?

Snub Cube

Rhombic Triacontahedron

Voting ended onJan 19, 2024

Propaganda

Snub Cube:

Also called the Snub Cuboctahedron

Archimedean Solid

Semiregular

Dual of the Pentagonal Icositetrahedron

It has 6 square faces, 32 regular triangular faces, 60 edges, and 24 vertices.

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

Image Credit: Cyp

Rhombic Triacontahedron:

Also called the Triacontahedron

Catalan Solid

Dual of a quasiregular polyhedron

Dual of the Icosidodecahedron

It has 30 rhombic faces, 62 edges, and 32 vertices of two types.

One of the 9 edge-transitive convex polyhedra along with the 5 Platonic Solids, the 2 Quasiregular Convex Polyhedra, and the Rhombic Dodecahedron.

It has both the tumbling block quilt pattern and a five-pointed star on its surface.

Image Credit: Maxim Razin based on Cyp

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 5 (Finals)

Which shape is better?

Truncated Icosidodecahedron

Regular Icosahedron

Voting ended onJan 19, 2024

Propaganda

Truncated Icosidodecahedron:

Also called the Rhombitruncated Icosidodecahedron, Great Rhombicosidodecahedron, Omnitruncated Dodecahedron, Omnituncated Icosahedron

Archimedean Solid

Semiregular

Dual of the Disdyakis Triacontahedron

It has 12 regular decagonal faces, 20 regular hexagonal faces, 30 square faces, 180 edges, and 120 vertices.

It has the most edges and vertices of all platonic and archimedean solids.

Of the vertex-transitive polyhedra, it fills up the most of the volume of the sphere it fits in (89.80%).

It is not actually the shape you get when you truncate an icosidodecahedron, although it is topologically equivalent.

It is the mod's favorite three-dimensional shape.

They made a void truncated icosidodecahedron and it's glorious. I had one for a while, it's hard to turn because of alignment issues, especially the decagonal sides. Fun puzzle tho, never did figure out how to permute the last layer...

Image Credit: @anonymous-leemur

Regular Icosahedron:

Platonic Solid

Regular

Dual of the Regular Dodecahedron

It has 20 regular triangular faces, 30 edges, and 12 vertices.

Image Credit: @etirabys

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 5 (Finals)

Which shape is better?

Truncated Icosidodecahedron

Regular Icosahedron

Voting ended onJan 19, 2024

Propaganda

Truncated Icosidodecahedron:

Also called the Rhombitruncated Icosidodecahedron, Great Rhombicosidodecahedron, Omnitruncated Dodecahedron, Omnituncated Icosahedron

Archimedean Solid

Semiregular

Dual of the Disdyakis Triacontahedron

It has 12 regular decagonal faces, 20 regular hexagonal faces, 30 square faces, 180 edges, and 120 vertices.

It has the most edges and vertices of all platonic and archimedean solids.

Of the vertex-transitive polyhedra, it fills up the most of the volume of the sphere it fits in (89.80%).

It is not actually the shape you get when you truncate an icosidodecahedron, although it is topologically equivalent.

It is the mod's favorite three-dimensional shape.

They made a void truncated icosidodecahedron and it's glorious. I had one for a while, it's hard to turn because of alignment issues, especially the decagonal sides. Fun puzzle tho, never did figure out how to permute the last layer...

Image Credit: @anonymous-leemur

Regular Icosahedron:

Platonic Solid

Regular

Dual of the Regular Dodecahedron

It has 20 regular triangular faces, 30 edges, and 12 vertices.

Image Credit: @etirabys

[wanderingandfound]

Attack! Kill the icosahedron! Send all prisoners to the void contained within us!

[wanderingandfound]

Great Rhombicosidodecahedra, assemble! We roll out at dawn!

[Image description: 8 colorations of the same art of a truncated icosidodecahedron done in the default tumblr style. Half of them have open eyes, half of them have closed eyes. Some of them are done in Pride flag colors, including an aromantic one, and aroace one, and two using Gilbert Baker's 2017 nine-stripe rainbow flag. End ID.]

Sorry Lee, I am using your creations for violent warfare.

[wanderingandfound]

#regular icosahedron looks like a hexagon #and hexagons are the bestagon

Hexagons are the bestagon, and that is why people should vote for the Truncated Icosidodecahedron. Because it has twenty (20) hexagons while the Regular Icosahedron has none (0).

⬣

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 5 (Finals)

Which shape is better?

Truncated Icosidodecahedron

Regular Icosahedron

Voting ended onJan 19, 2024

Propaganda

Truncated Icosidodecahedron:

Also called the Rhombitruncated Icosidodecahedron, Great Rhombicosidodecahedron, Omnitruncated Dodecahedron, Omnituncated Icosahedron

Archimedean Solid

Semiregular

Dual of the Disdyakis Triacontahedron

It has 12 regular decagonal faces, 20 regular hexagonal faces, 30 square faces, 180 edges, and 120 vertices.

It has the most edges and vertices of all platonic and archimedean solids.

Of the vertex-transitive polyhedra, it fills up the most of the volume of the sphere it fits in (89.80%).

It is not actually the shape you get when you truncate an icosidodecahedron, although it is topologically equivalent.

It is the mod's favorite three-dimensional shape.

They made a void truncated icosidodecahedron and it's glorious. I had one for a while, it's hard to turn because of alignment issues, especially the decagonal sides. Fun puzzle tho, never did figure out how to permute the last layer...

Image Credit: @anonymous-leemur

Regular Icosahedron:

Platonic Solid

Regular

Dual of the Regular Dodecahedron

It has 20 regular triangular faces, 30 edges, and 12 vertices.

Image Credit: @etirabys

[wanderingandfound]

Attack! Kill the icosahedron! Send all prisoners to the void contained within us!

[wanderingandfound]

Great Rhombicosidodecahedra, assemble! We roll out at dawn!

[Image description: 8 colorations of the same art of a truncated icosidodecahedron done in the default tumblr style. Half of them have open eyes, half of them have closed eyes. Some of them are done in Pride flag colors, including an aromantic one, and aroace one, and two using Gilbert Baker's 2017 nine-stripe rainbow flag. End ID.]

Sorry Lee, I am using your creations for violent warfare.

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 5 (Third Place)

Which shape is better?

Snub Cube

Rhombic Triacontahedron

Voting ended onJan 19, 2024

Propaganda

Snub Cube:

Also called the Snub Cuboctahedron

Archimedean Solid

Semiregular

Dual of the Pentagonal Icositetrahedron

It has 6 square faces, 32 regular triangular faces, 60 edges, and 24 vertices.

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

Image Credit: Cyp

Rhombic Triacontahedron:

Also called the Triacontahedron

Catalan Solid

Dual of a quasiregular polyhedron

Dual of the Icosidodecahedron

It has 30 rhombic faces, 62 edges, and 32 vertices of two types.

One of the 9 edge-transitive convex polyhedra along with the 5 Platonic Solids, the 2 Quasiregular Convex Polyhedra, and the Rhombic Dodecahedron.

It has both the tumbling block quilt pattern and a five-pointed star on its surface.

Image Credit: Maxim Razin based on Cyp

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 5 (Finals)

Which shape is better?

Truncated Icosidodecahedron

Regular Icosahedron

Voting ended onJan 19, 2024

Propaganda

Truncated Icosidodecahedron:

Also called the Rhombitruncated Icosidodecahedron, Great Rhombicosidodecahedron, Omnitruncated Dodecahedron, Omnituncated Icosahedron

Archimedean Solid

Semiregular

Dual of the Disdyakis Triacontahedron

It has 12 regular decagonal faces, 20 regular hexagonal faces, 30 square faces, 180 edges, and 120 vertices.

It has the most edges and vertices of all platonic and archimedean solids.

Of the vertex-transitive polyhedra, it fills up the most of the volume of the sphere it fits in (89.80%).

It is not actually the shape you get when you truncate an icosidodecahedron, although it is topologically equivalent.

It is the mod's favorite three-dimensional shape.

They made a void truncated icosidodecahedron and it's glorious. I had one for a while, it's hard to turn because of alignment issues, especially the decagonal sides. Fun puzzle tho, never did figure out how to permute the last layer...

Image Credit: @anonymous-leemur

Regular Icosahedron:

Platonic Solid

Regular

Dual of the Regular Dodecahedron

It has 20 regular triangular faces, 30 edges, and 12 vertices.

Image Credit: @etirabys

[best-shapes]

Regular-ish Convex Polyhedra (with bonus sphere) Bracket

Round 4 had 136 votes votes over 2 polls. And with that we have come to the finals! Thank you to everyone who has voted in these polls, rest assured I have plans for more shape brackets. In the meantime, you can submit your favorite shape here.

Round 4:

Truncated Icosidodecahedron vs Regular Icosahedron

Battle for third place: Snub Cube vs Rhombic Triacontahedron

Round 1 Masterpost. Round 2 Masterpost. Round 3 Masterpost. Round 4 Masterpost.