#polyhedra
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Polyhedron cards
#polyhedra#polyhedron#geometry#shapes#knottys mathy stuffy#knottys math art#math art#stim toy#math love#math passion#math happiness#math#art#isometric#cards
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Regular-ish Convex Polyhedra Bracket — Round 5 (Finals)
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
#Round 5#Truncated Icosidodecahedron#Great Rhombicosidodecahedron#Regular Icosahedron#Icosahedron#Polyhedra#Archimedean Solids#Platonic Solids
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some assorted angels i thought were very beautiful.
the program is poly 1.12! i highly recomend for polyhedra viewing. its super cool and has so many!!! you can choose the color of the faces as well. you can get it for free at peda.com (pedagoguery software).
incase the text is too small the shapes in order are:
6-frequency icosahedral geodesic hemishere
6-frequency octahedral geodesic sphere
6-frequency icosahedral geodesic sphere
also yay my first post on this blog!!! :]
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Quick friend-shapes needed to be made.
(meaning: I was bored and needed to do something with my hands and brain.)
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the Elongated square gyrobicupola! gotta be one of my favorite genders
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thinkin about pentagonal rotunda
pe- pero
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N-simplex? Actually I find it quite complicated.
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MOVABLE
Mathober Day 22: Movable.
Originally I was going to do removable, but searching MathWorld for movable found this cool flexible polyhedron. Convex polyhedra have been shown to be rigid, but concave polyhedra can flex. Mathworld suggested this one.
Dashed lines are valley folds, interior solid lines are mountain folds, outside edges are whatever makes it work. Regardless, pretty fun tetradecahedron. I left tabs on alternating edges to help tape it together.
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Hi, Math Tumblr!
Question first, than I will allow myself to ramble.
Are there names for the families of polytopes¹? Triangle based polytopes are simplexes, square based are hypercubes and orthoplexes, the demicubes are, I guess, demicubes. (I do not yet understand demicubes.) But do 24, 120, and 600-cells have matching group names with their higher and lower dimensional counterparts?
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Me and my weird little kids love shapes. My youngest also loves collecting and my eldest loves trading (but mostly cubes. Trading is a way to get more cubes). For the last 2 years, I've been making my kids collectible trading cards of convex polyhedra.
If they get a full set (like the 5 platonic solids, the 3 pyramids, or the 8 antiprisms [we don't use any regular polygons above the decagon]) they can trade them in for a special card. In an effort to provide more cubes (there's only one. So it's been a challenge) the special cards are the fundamental complex and regular polytopes in dimensions 3 to 10.
But I don't know much about extra dimensions. My math skills mostly stopped developing when schools brought in the math that requires calculators and ~shiver~ evil decimals. (With a brief glowing resurgence for some aspects of linear algebra in university. Beautiful matrices!) While I COULD just make a set of hypercubes, my completionist tendencies do not accept this. Can anyone tell me if there are names I could use for sets for each of the uniform polychorons?
Additional appreciated information:
Do any of the higher dimensions have a specific term for their polytopes? (Including old terms that aren't often used but sound cool.)
Are there any fun visualization for higher dimensional polytopes? I can use orthographic representations, but anything with pseudo-3D would be more appealing to the kids. Also, do you know somewhere I could find such things online? Currently, I am using wikipedia. I like sets to have consistent visuals with each other, but they don't always need to be consistent with the rest of the cards.
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¹for the non-math weirdos: 'polytopes' are objects with flat sides (faces). A 2D object is a 'polygon', a 3D object is a 'polyhedron', and 4D things like the tesseract from the Marvel movies are 'polychorons'. You can keep adding dimensions forever.
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i want a chess set in which all the pieces are obscure polyhedra. watch as i move my small icosihemidodecahedron to g8 and promote it to great truncated icosidodecahedron. what delightful fun
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Great stellated dodecahedron
For that Kepler-Poinsot-Polyhedron I started to draw an icosahedron and continued to add triangular pyramids as "hats" on top of each of the 20 triangular icosahedron faces.
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This is the Small Stellated Dodecahedron I drew a while back:
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How are the Dodecahedron, Icosahedron, Small and Great Stellated Dodecahedron related?
(Source)
Truncation of the Small Stellated Dodecahedron:
Truncation of the Great Stellated Dodecahedron:
#kepler-poinsot-polyhedra#polyhedra#polyhedron#shapes#shape#stellated#stellated polyhedron#geometry#mathy stuffy#mathy#math#artsy math#artsy mathy#knottys math#kepler-poinsot-polyhedron
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Regular-ish Convex Polyhedra Bracket — Round 3
Propaganda
Regular Tetrahedron:
Also called the Triangular Pyramid
Platonic Solid
Regular
Dual of the Regular Tetrahedron
It has 4 regular triangular faces, 6 edges, and 4 vertices.
Self-Dual
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.
Image Credit: Maxim Razin based on Cyp
#Round 3#Regular Tetrahedron#Tetrahedron#Rhombic Triacontahedron#Platonic Solids#Catalan Solids#Polyhedra
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At 90 units, this is one of the largest modular pieces I've made. Truncated icosahedron (⚽ shape) made from Tom Hull's PHiZZ unit. No glue involved and yes, it's gay.
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Polyhedron info collection
I started to collect the polyhedra infos and drawings into this file.
This is the General frame of the info pages:
(And this is my empty sample page for copying:)
That is the one I drew today:
The pages can be unfolded like that and filled with more infos, if I decide to include more infos in the future:
The first page of my folder is a tiny bag with colorful foldable nets inside:
That is my progress so far:
(Drawing the nets is the least enjoyable task for me, as I need to draw them very tiny, and it sucks to draw in such a tiny size, therefore I procrastinate on that... )
#polyhedron#polyhedron info collection#polyhedra#geometry#math#mathy#mathematics#info collection#info collecting
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i want to make a little polyhedron plushie!!
which polyhedra do you think will be more conducive to plushing? the easiest (i think) would be to make a (companion) cube, but i don't want to accidentally have a sphere 0_0
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Note
almost you in the middle tumblr.com/catboybeebop/736942982628098048
holy shit your right
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