The rhombic icosahedron is a polyhedron shaped like an oblate sphere. Its 20 faces are congruent golden rhombi; 3, 4, or 5 faces meet at each vertex. It has 5 faces (green on top figure) meeting at each of its 2 poles; these 2 vertices lie on its axis of 5-fold symmetry, which is perpendicular to 5 axes of 2-fold symmetry through the midpoints of opposite equatorial edges (example on top figure: most left-hand and most right-hand mid-edges). Its other 10 faces follow its equator, 5 above and 5 below it; each of these 10 rhombi has 2 of its 4 sides lying on this zig-zag skew decagon equator. The rhombic icosahedron has 22 vertices. It has D5d, [2+,10], (2*5) symmetry group, of order 20; thus it has a center of symmetry (since 5 is odd). Even though all its faces are congruent, the rhombic icosahedron is not face-transitive, since one can distinguish whether a particular face is near the equator or near a pole by examining the types of vertices surrounding this face. (Wikipedia).
How to Construct an Icosahedron
How the greeks constructed the icosahedron. Source: Euclids Elements Book 13, Proposition 16. In geometry, a regular icosahedron is a convex polyhedron with 20 faces, 30 edges and 12 vertices. It is one of the five Platonic solids, and the one with the most faces. https://www.etsy.com/lis
From playlist Platonic Solids
Using the pythagorean theorem to a rhombus
π Learn how to solve problems with rhombuses. A rhombus is a parallelogram such that all the sides are equal. Some of the properties of rhombuses are: all the sides are equal, each pair of opposite sides are parallel, each pair of opposite angles are equal, the diagonals bisect each other,
From playlist Properties of Rhombuses
Platonic and Archimedean solids
Platonic solids: http://shpws.me/qPNS Archimedean solids: http://shpws.me/qPNV
From playlist 3D printing
How to determine if points are a rhombus, square or rectangle
π Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
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
Paul Hildebrandt - Richert - Baer - Pelletier - G4G14 Apr 2022
A tribute to the men who created the Zometool.
From playlist G4G14 Videos
Applying the properties of a rhombus to determine the length of a diagonal
π Learn how to solve problems with rhombuses. A rhombus is a parallelogram such that all the sides are equal. Some of the properties of rhombuses are: all the sides are equal, each pair of opposite sides are parallel, each pair of opposite angles are equal, the diagonals bisect each other,
From playlist Properties of Rhombuses
The Collapse of Viruses: Graph-Based Percolation Theory in the Wolfram Language
Graph-based percolation theory may be done in the Wolfram Language, here to aid in the understanding of viruses, their disassembly and eventual collapse. Capsids are protein nanocontainers that store and protect a virusβs genetic material in transit between hosts. Capsids consist of hundre
From playlist Wolfram Technology Conference 2020
What are the properties that make up a rhombus
π Learn how to solve problems with rhombuses. A rhombus is a parallelogram such that all the sides are equal. Some of the properties of rhombuses are: all the sides are equal, each pair of opposite sides are parallel, each pair of opposite angles are equal, the diagonals bisect each other,
From playlist Properties of Rhombuses
The cube shadow theorem (pt.2): The best hypercube shadows
NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Make sure to watch part 1 of this video before you watch part 2: https://youtu.be/rAHcZGjKVvg In this s
From playlist Recent videos
The unexpected logic behind rolling multiple dice and picking the highest.
Check out Jane Street's icosahedron puzzle: https://www.janestreet.com/IMO2022/ 2022 International Mathematical Olympiad! https://www.imo2022.org/ If you want those d60 and d120 we sell them on Maths Gear or you can go direct to The Dice Lab. https://mathsgear.co.uk/collections/dice http
From playlist Prob and Stats
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
Avoiding math to have a relaxing Saturday with friends. Links to everyone's cool stuff below: Gwen Fisher: http://www.beadinfinitum.com/ She also has a blog: http://gwenbeads.blogspot.com/ Also buy everything from her etsy shop before someone else does: https://www.etsy.com/shop/gwenbead
From playlist Thanksgiving: Edible Math
Perfect Shapes in Higher Dimensions - Numberphile
Carlo Sequin talks through platonic solids and regular polytopes in higher dimensions. More links & stuff in full description below βββ Extra footage (Hypernom): https://youtu.be/unC0Y3kv0Yk More videos with with Carlo: http://bit.ly/carlo_videos Edit and animation by Pete McPartlan Pete
From playlist Carlo SΓ©quin on Numberphile
Determining if a set of points is a rhombus, square or rectangle
π Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Eleftherios Pavlides - Elastegrity Geometry of Motion - G4G13 Apr 2018
"The Chiral Icosahedral Hinge Elastegrity resulted from a Bauhaus paper folding exercise, that asks material and structure to dictate form. The key new object obtained in 1982 involved cutting slits into folded pieces of paper and weaving them into 8 irregular isosceles tetrahedra, attache
From playlist G4G13 Videos
The Search for Natural Quasicrystals - Paul Steinhardt
Paul Steinhardt Center for Theoretical Science, Princeton University March 7, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
The remarkable Platonic solids II: symmetry | Universal Hyperbolic Geometry 48 | NJ Wildberger
We look at the symmetries of the Platonic solids, starting here with rigid motions, which are essentially rotations about fixed axes. We use the normalization of angle whereby one full turn has the value one, and also connect the number of rigid motions with the number of directed edges.
From playlist Universal Hyperbolic Geometry
Roger Penrose: Forbidden crystal symmetry - Event Q&A
The event question and answer session from an Ri event with Sir Roger Penrose in October 2013. The famous mathematician provides a unique insight into the "forbidden symmetry" of his famous penrose tiles and the use of non-repeating patterns in design and architecture. It is a rigorous
From playlist Celebrating Crystallography
How to determine if a set of points is a rectangle, rhombus or square
π Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane