In geometry, the medial rhombic triacontahedron (or midly rhombic triacontahedron) is a nonconvex isohedral polyhedron. It is a stellation of the rhombic triacontahedron, and can also be called small stellated triacontahedron. Its dual is the dodecadodecahedron. Its 24 vertices are all on the 12 axes with 5-fold symmetry (i.e. each corresponds to one of the 12 vertices of the icosahedron). This means that on each axis there is an inner and an outer vertex. The ratio of outer to inner vertex radius is , the golden ratio. It has 30 intersecting rhombic faces, which correspond to the faces of the convex rhombic triacontahedron. The diagonals in the rhombs of the convex solid have a ratio of 1 to . The medial solid can be generated from the convex one by stretching the shorter diagonal from length 1 to . So the ratio of rhomb diagonals in the medial solid is 1 to . This solid is to the compound of small stellated dodecahedron and great dodecahedron what the convex one is to the compound of dodecahedron and icosahedron:The crossing edges in the dual compound are the diagonals of the rhombs.The faces have two angles of , and two of . Its dihedral angles equal . Part of each rhomb lies inside the solid, hence is invisible in solid models. (Wikipedia).
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
Amazing Science Toys/Gadgets 6
New Video ๐๐ป https://youtu.be/k_i_c9OUJKE Hi Everyone :) Welcome back! I get asked often: "Where did you get all this stuff?" My goal is to share the real magic of science and physics- and to this end I will update here (and in my store) suggestions on where to get some of these toys
From playlist Amazing Science Toys/Gadgets
Using the pythagorean theorem to a rhombus
๐ 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
Fair Dice (Part 1) - Numberphile
Probability expert Professor Persi Diaconis (Stanford University) talking about dice. More links & stuff in full description below โโโ Part 2: https://youtu.be/8UUPlImm0dM Tadashi and Dice: https://youtu.be/zzKGnuvX6IQ More dice videos: http://bit.ly/Dice_Videos More Persi Diaconi videos:
From playlist Persi Diaconis on Numberphile
Using a set of points determine if the figure is a parallelogram using the midpoint formula
๐ 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
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 โโโ 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 Sรฉquin on Numberphile
How to determine if points are a rhombus, square or rectangle
๐ 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
Applying the properties of a rhombus to determine the length of a diagonal
๐ 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
What are the trigonometric definitions of a right triangle
๐ Learn all about the trigonometry of right triangles. A right triangle is a triangle that has 90 degrees as one of its angles. The trigonometric identities of right triangles give us the relationship between the angles of a right triangle and the side lengths of the right triangle. These
From playlist Right Triangle Trigonometry | Learn About
Using the slope formula to determine if points make up a rectangle
๐ 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
Determining if a set of points makes a parallelogram or not
๐ 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
Determining if a set of points is a rhombus, square or rectangle
๐ 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
Live demo https://codepen.io/thebabydino/pen/OJmmwrz If the work I've been putting out since early 2012 has helped you in any way or you just like it, please consider supporting it to help me continue and stay afloat. You can do so in one of the following ways: * you can be a cool cat ๐ผ๐ฉ
From playlist Basic Tips & Tricks
Determine if a set of points is a parallelogram by using the slope formula
๐ 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
See http://thedicelab.com/ for more details. These dice are available at http://www.mathartfun.com/shopsite_sc/store/html/DiceLabDice.html
From playlist Dice
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
Laura Taalman - 3D printed Hinged Dissections and Foldable Polyhedra - CoM Apr 2021
Weโll talk briefly about 3D printing foldable and hinged models for polygonal and polyhedral dissections, and a new idea for โvolume netsโ for which I am seeking feedback. Included will be access to 3D design files that people can use to create their own models. Q&A at the end can extend t
From playlist Celebration of Mind 2021
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 virusโs genetic material in transit between hosts. Capsids consist of hundre
From playlist Wolfram Technology Conference 2020
Determine if a set of points is a parallelogram using the distance formula
๐ 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