Catalan solids | Geodesic polyhedra

Pentakis dodecahedron

In geometry, a pentakis dodecahedron or kisdodecahedron is the polyhedron created by attaching a pentagonal pyramid to each face of a regular dodecahedron; that is, it is the Kleetope of the dodecahedron. It is a Catalan solid, meaning that it is a dual of an Archimedean solid, in this case, the truncated icosahedron. (Wikipedia).

Pentakis dodecahedron
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How to Construct a Dodecahedron

How the greeks constructed the Dodecahedron. Euclids Elements Book 13, Proposition 17. In geometry, a dodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. A regular dode

From playlist Platonic Solids

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Regular polyhedra

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/q0PF.

From playlist 3D printing

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Canonical structures inside the Platonic solids III | Universal Hyperbolic Geometry 51

The dodecahedron is surely one of the truly great mathematical objects---revered by the ancient Greeks, Kepler, and many mathematicians since. Its symmetries are particularly rich, and in this video we look at how to see the five-fold and six-fold symmetries of this object via internal str

From playlist Universal Hyperbolic Geometry

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How to construct a Tetrahedron

How the greeks constructed the first platonic solid: the regular tetrahedron. Source: Euclids Elements Book 13, Proposition 13. In geometry, a tetrahedron also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. Th

From playlist Platonic Solids

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The Pop-up Dodecahedron

Instruction to download http://singingbanana.com/popupdodecahedron.pdf More information about the dodecahedron that I would have like to have gone into in this video http://uk.youtube.com/watch?v=-lqpSpje42o Dodecahedron at wikipedia http://en.wikipedia.org/wiki/Dodecahedron Plato

From playlist My Maths Videos

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Isosceles Triangle Theorem: Dynanic Desmos Illustrator

Isosceles triangle theorem animation & explorer made in #Desmos. https://teacher.desmos.com/activitybuilder/custom/60742b18afd8ae0d274b6efb #MTBoS #ITeachMath #math

From playlist Desmos Activities, Illustrations, and How-To's

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Sierpinski from Pascal

This is a recreation of a short clip from a long form video showing six different ways to construct the Sierpinski triangle: https://youtu.be/IZHiBJGcrqI In this short, we shade odd entries of the Halayuda/Pascal triangle to obtain the Sierpinski triangle. Can you explain why this works?

From playlist Fractals

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How to construct a Regular Hexahedron (Cube)

How the greeks constructed the 3rd platonic solid: the regular hexahedron Source: Euclids Elements Book 13, Proposition 15 https://www.etsy.com/listing/1037552189/wooden-large-platonic-solids-geometry

From playlist Platonic Solids

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Math Mornings at Yale: Asher Auel - Wallpaper, Platonic Solids, and Symmetry

The Platonic solids-the tetrahedron, cube, octahedron, dodecahedron, and icosahedron-are some of the most beautiful and symmetric geometrical objects in 3-dimensional space. Their mysteries started to be unraveled by the ancient Greeks and still fascinate us today. In 1872, the German geom

From playlist Math Mornings at Yale

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Dodecahedron of Demolition

Demolition with dodecahedrons of various masses, trajectories, and velocities.

From playlist Physics

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Inside-Out Logic

A fold-up, slice-and-dice dodecahedron and its complement. With a 3D printer, you can make your own using the files here: http://georgehart.com/rp/T-O-M/t-o-m.html

From playlist Odds and Ends

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AlgTop9: Applications of Euler's formula and graphs

We use Euler's formula to show that there are at most 5 Platonic, or regular, solids. We discuss other types of polyhedra, including deltahedra (made of equilateral triangles) and Schafli's generalizations to higher dimensions. In particular in 4 dimensions there is the 120-cell, the 600-c

From playlist Algebraic Topology: a beginner's course - N J Wildberger

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Amina Buhler - The Magic of Polytopes-Mandalas - CoM July 2021

Polytopes are 3-Dimensional shadows from higher dimensional polyhedra (4-Dimensional & above). These 3-D shadows, when rotated suddenly out of chaos, line-up & reveal, cast mandala patterns into 2-D of 2,3, & 5-fold symmetry. While constructing a stainless steel 120-cell (4-D dodecahed

From playlist Celebration of Mind 2021

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Hypernom.com talk at Bridges 2015 in Baltimore (Rectangular version)

Talk I gave with Vi Hart and Andrea Hawksley on the virtual reality artgame "Hypernom" we made with Marc ten Bosch. The game is playable at http://hypernom.com. Slides for the talk: http://math.okstate.edu/people/segerman/talks/hypernom_talk.pdf Spherical version of the video: https://ww

From playlist GPU shaders

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Jane Kostick - Coordinated Motion Around a Dodecahedron - G4G12 April 2016

The presentation included a demonstration of wooden sculptures that come apart in two-stages, like a coordinated motion puzzle. They are composed of four sets of a dozen sticks surrounding a 12-sided block.

From playlist G4G12 Videos

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Cardboard Tetrahedron Pyramid Perfect Circle Solar How to make a pyramid out of cardboard

How to make a pyramid out of cardboard. A tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex.

From playlist HOME OF GREENPOWERSCIENCE SOLAR DIY PROJECTS

Related pages

Archimedean solid | Excavated dodecahedron | Pentagonal pyramid | Regular icosahedron | Truncated icosahedron | Geometry | Kleetope | Dual polyhedron | Regular dodecahedron | Golden ratio | Catalan solid