Johnson solids

Pentagonal gyrocupolarotunda

In geometry, the pentagonal gyrocupolarotunda is one of the Johnson solids (J33). Like the pentagonal orthocupolarotunda (J32), it can be constructed by joining a pentagonal cupola (J5) and a pentagonal rotunda (J6) along their decagonal bases. The difference is that in this solid, the two halves are rotated 36 degrees with respect to one another. 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. (Wikipedia).

Pentagonal gyrocupolarotunda
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How to find the volume of a pentagonal pyramid

👉 Learn how to find the volume and the surface area of a pyramid. A pyramid is a 3-dimensional object having a polygon as its base and triangular surfaces converging at a single point called its apex. A pyramid derives its name from the shape of its base, i.e. a pyramid with a triangular b

From playlist Volume and Surface Area

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Determining if a set of points makes a parallelogram or not

👉 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

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How to determine if a set of points makes up a rectangle using the distance 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

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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

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Determine if a set of points makes up a rectangle using the distance 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

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The Chaos Game in Pentagon, Octagon, and Square (math visualization)

To buy me a coffee, head over to https://www.buymeacoffee.com/VisualProofs Thanks! In this video, we explore the differences between starting with a random dot in a regular pentagon, octagon, and square and iterating the procedure of choosing a vertex (or midpoint for square) at random a

From playlist Fractals

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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

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Determine if a set of points is a trapezoid or not

👉 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

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How to determine if a set of points is a rectangle, rhombus or square

👉 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

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Ayliean MacDonald - The Pentagon: A User’s Guide - CoM Oct 2021

Regular pentagons throw a spanner in the works when it comes to tessellation but don’t let that one case tarnish the good name of the pentagon! Come along as we explore the 15 irregular pentagons which do tile the plane, journey through five fold symmetry, make a quick pit stop to look at

From playlist Celebration of Mind 2021

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Glen Whitney - Convex Pintegon Tilings - CoM Oct 2021

Tiling the plane with convex pentagons has a rich mathematical history in which Martin Gardner and a diverse cast of other participants play key roles. Broad audiences can appreciate the associated questions, and enjoy the beautiful images that the answers yield. All of these characteristi

From playlist Celebration of Mind 2021

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D. Davis - Periodic paths on the pentagon

Mathematicians have long understood periodic trajectories on the square billiard table. In the present work, we describe periodic trajectories on the regular pentagon – their geometry, symbolic dynamics, and group structure. Some of the periodic trajectories exhibit a surprising

From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications

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Do Facts Matter in Storytelling?

From the mediaX Seminar, Science Storytelling & the Contagion of Ideas, journalist Jamie McIntyre shares how his reporting of the Pentagon attack on 9-11 was taken out of context, and how this event lead him on a decade long journey to try to better understand the limits of factual informa

From playlist Science Storytelling and the Contagion of Ideas

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Diana Davis: Billiards on regular polygons

HYBRID EVENT Recorded during the meeting "Differential Geometry, Billiards, and Geometric Optics" the October 04, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathemat

From playlist Dynamical Systems and Ordinary Differential Equations

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Laura Taalman - Printing Perfect Pentagons - G4G13 Apr 2018

So we know there are 15 families of pentagonal tessellations… how do we 3D print models based on those tessellations?

From playlist G4G13 Videos

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Bob Hearn - There Are Only 15 - G4G13 Apr 2018

Notes on the proof that there are only 15 convex pentagons that tile the plane.

From playlist G4G13 Videos

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Frank Morgan - Optimal Pentagonal Tilings - CoM May 2021

In 2001 Thomas Hales proved that hexagons provide the least-perimeter way to tile the plane with unit areas. Of course, among hexagons, the regular one is best. Similarly, the best quadrilateral is square and the best triangle is equilateral. But what is the best pentagonal tile? Unfortuna

From playlist Celebration of Mind 2021

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How to determine the perimeter of a quadrilateral using distance formula of four points

👉 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

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A 100 YEAR OLD PROBLEM AND ITS 15 SOLUTIONS: Pentagons and Tiling | ND

Today we look at a 100+ year old problem and its 15 solutions. The 100 year old math problem being the convex monohedral pentagonal tiling problem the only open case of the convex monohedral tiling problem. Pentagons have been a point of interest in the study of tiling for a while due to t

From playlist The New CHALKboard

Related pages

Pentagon | Decagon | Convex polytope | Pentagonal cupola | Pentagonal orthocupolarotunda | Pentagonal orthobirotunda | Surface area | Geometry | Johnson solid | Regular polygon | Triangle | Volume | Formula | Pentagonal rotunda