In geometry, the parabidiminished rhombicosidodecahedron is one of the Johnson solids (J80). It is also a canonical polyhedron. A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966. It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae removed. Related Johnson solids are the diminished rhombicosidodecahedron (J76) where one cupola is removed, the metabidiminished rhombicosidodecahedron (J81) where two non-opposing cupolae are removed, and the tridiminished rhombicosidodecahedron (J83) where three cupolae are removed. (Wikipedia).
Using the pythagorean theorem to a rhombus
👉 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
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
In this video we review the basic components of a parabola
From playlist Parabolas
How to determine the domain and range and graph
👉 Learn about the parts of a parabola. A parabola is the shape of the graph of a quadratic equation. A regular palabola is the parabola that is facing either up or down while an irregular parabola faces left or right. A quadratic equation is an equation whose highest exponent in the variab
From playlist Find the Parts of a Parabola
What are Hyperbolas? | Ch 1, Hyperbolic Trigonometry
This is the first chapter in a series about hyperbolas from first principles, reimagining trigonometry using hyperbolas instead of circles. This first chapter defines hyperbolas and hyperbolic relationships and sets some foreshadowings for later chapters This is my completed submission t
From playlist Summer of Math Exposition 2 videos
Using a set of points determine if the figure is a parallelogram using the midpoint formula
👉 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
Using are pythagorean identites to simplify an expression
👉 Learn how to simplify identities by factoring. Just like in normal algebraic expressions, trigonometric identities can be simplified by factoring out the GCFs from the terms of the identities, then common trigonometric identities like the quotient, reciprocal, even, odd, co-function, and
From playlist Simplify Trigonometric Identities
How to determine if points are a rhombus, square or rectangle
👉 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
Determine the vertex and domain and range of a function
👉 Learn about the parts of a parabola. A parabola is the shape of the graph of a quadratic equation. A regular palabola is the parabola that is facing either up or down while an irregular parabola faces left or right. A quadratic equation is an equation whose highest exponent in the variab
From playlist Find the Parts of a Parabola
Class 5: Tessellations & Modulars
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This class introduces more examples of origami models that use a variety of techniques and media. At the end of the session, the c
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
Dissecting a Playdough Rhombic Dodecahedron with Miles
This is a playful demonstration of how a rhombic dodecahedron can be diced up and the pieces rearranged to make three of the Platonic solids. Three cuts yield eight pieces that form two cubes. Four cuts yield 14 pieces that form two tetrahedrons and one octahedron. Special thanks to 10-
From playlist Recreational Math Videos