In 4-dimensional geometry, the dodecahedral pyramid is bounded by one dodecahedron on the base and 12 pentagonal pyramid cells which meet at the apex. Since a dodecahedron's circumradius is greater than its edge length, the pentagonal pyramids require tall isosceles triangle faces. The dual to the dodecahedral pyramid is an icosahedral pyramid, seen as an icosahedral base, and 20 regular tetrahedra meeting at an apex. (Wikipedia).
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
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
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
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
How do ceramic crystal structures differ from metal crystal structures?
Metal crystal structures are much simpler than ceramic structures. This is due to two reasons. First, ceramics have positive and negative charged ions. Cations and ions must maintain charge neutrality. Second, the size of cations and anions are very different! Structures with multiple diff
From playlist Materials Sciences 101 - Introduction to Materials Science & Engineering 2020
Learn how to determine the surface area of a triangular 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
Finding the volume and surface area of a pyramid with a rectangular base
👉 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
0:00 coordination of hexagonal close-packed HCP structure 4:40 theoretical density 21:37 structure of ceramics using cation/anion ratio 30:65 NaCl rock salt structure 33:05 CsCl structure 35:18 ZnS zinc blende structure 39:00 solving for lattice parameter in terms of cation and anion radii
From playlist Introduction to Materials Science & Engineering Fall 2019
Henry Segerman - 3D Shadows: Casting Light on the Fourth Dimension - 02/11/17
Henry Segerman "3D Shadows: Casting Light on the Fourth Dimension" February 11, 2017 Wesier Hall Ann Arbor, Michigan
From playlist 3D printing
Learn how to determine the surface area of a triangular prism
👉 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
Day 14 ceramic crystal structures
0:00 reading quiz 5:25 HCP structure and close-packing 10:27 theoretical density calculation 15:00 difference between observed and theoretical densities 18:16 ceramic crystal structures and using rc/ra ratio to determine coordination 23:26 rock salt (NaCl) structure 29:28 cesium chloride (
From playlist Introduction to Materials Science and Engineering Fall 2017
Combinatorics and Geometry to Arithmetic of Circle Packings - Nakamura
Speaker: Kei Nakamura (Rutgers) Title: Combinatorics and Geometry to Arithmetic of Circle Packings Abstract: The Koebe-Andreev-Thurston/Schramm theorem assigns a conformally rigid fi-nite circle packing to a convex polyhedron, and then successive inversions yield a conformally rigid infin
From playlist Mathematics
How to find the surface area of a 3D 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
This shows a 3d print of a puzzle I produced using shapeways.com. This is joint work with Saul Schleimer. This is available at http://shpws.me/lmxi. A larger version of the puzzle is available at http://shpws.me/lmxi.
From playlist 3D printing
Available from Shapeways: https://www.shapeways.com/shops/henryseg?section=Holonomy+mazes Thanks to Sabetta Matsumoto and Chaim Goodman-Strauss for building the sculpture, to Saul Schleimer for naming the "rook", and to all of them for helpful conversations.
From playlist 3D printing
To Build Viruses: A Markov Chain Monte Carlo Algorithm for Stimulating Viral Assembly Kinetics
For the latest information, please visit: http://www.wolfram.com Speaker: Nicholas Brunk Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile devices, and more.
From playlist Wolfram Technology Conference 2015
How do you find the surface area of a 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
Bridges 2014 talk: The quaternion group as a symmetry group
This is a talk I gave at the Bridges conference on mathematics and the arts (http://bridgesmathart.org/), on 18th August 2014, about my paper with Vi Hart with the same title. The slides are available at https://www.math.okstate.edu/~segerman/talks/quaternion_group_as_a_symmetry_group.pdf
From playlist 3D printing
"Illustrating Geometry" exhibition at SCGP, Artist's talk: "Sculpture in four-dimensions"
Slides: http://www.math.okstate.edu/~segerman/talks/sculpture_in_4-dimensions.pdf This video is also available at the Simons Center website, at http://scgp.stonybrook.edu/archives/11540 Thanks to Josh Klein for filming and editing.
From playlist 3D printing
how to determine the surface area of a square 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