Space-filling polyhedra

Parallelohedron

In geometry, a parallelohedron is a polyhedron that can be translated without rotations in 3-dimensional Euclidean space to fill space with a honeycomb in which all copies of the polyhedron meet face-to-face. There are five types of parallelohedron, first identified by Evgraf Fedorov in 1885 in his studies of crystallographic systems: the cube, hexagonal prism, rhombic dodecahedron, elongated dodecahedron, and truncated octahedron. (Wikipedia).

Parallelohedron
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What are the properties that make up a parallelogram

👉 Learn how to solve problems with parallelograms. A parallelogram is a four-sided shape (quadrilateral) such that each pair of opposite sides are parallel and are equal. Some of the properties of parallelograms are: each pair of opposite sides are equal, each pair of opposite sides are pa

From playlist Properties of Parallelograms

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Using the properties of parallelograms to solve for the missing diagonals

👉 Learn how to solve problems with parallelograms. A parallelogram is a four-sided shape (quadrilateral) such that each pair of opposite sides are parallel and are equal. Some of the properties of parallelograms are: each pair of opposite sides are equal, each pair of opposite sides are pa

From playlist Properties of Parallelograms

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What is a parallel universe?

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From playlist Science Unplugged: Parallel Universes

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What are parallel lines and a transversal

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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What's a Parallelogram? Geometry Terms and Definitions

An introduction to the parallelogram, a fundamental geometric shape. Geometer: Louise McCartney Artwork: Kelly Vivanco Director: Michael Harrison Written & Produced by Kimberly Hatch Harrison and Michael Harrison ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www

From playlist Socratica: The Geometry Glossary Series

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Proving Parallel Lines with Angle Relationships

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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Properties of Parallelograms

I introduce the Properties of Parallelograms...the opposite sides are equal, the opposite angles are equal, the consecutive angles are supplementary, and the diagonals bisect each other. I work through four algebraic examples in this video at 4:28 14:30 Find free review test, useful notes

From playlist Geometry

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What is the Consecutive Interior Angle Converse Theorem

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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What is the Corresponding Angle Converse Theorem

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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What are the Angle Relationships for Parallel Lines and a Transversal

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

Related pages

Hexagon | Translation (geometry) | Coxeter–Dynkin diagram | Boris Delaunay | 24-cell | Truncated octahedron | Bravais lattice | Voronoi diagram | Zonohedron | Honeycomb (geometry) | Parallelogram | Rhombic dodecahedral honeycomb | Permutohedron | Rhombic dodecahedron | Affine transformation | Cube | Polyhedron | Parallelepiped | Hexagonal prism | Euclidean space | Minkowski problem for polytopes | Hermann Minkowski | Parallelogon | Bitruncated cubic honeycomb | Plesiohedron | Degeneracy (mathematics) | Elongated dodecahedron | Geometry | Cubic honeycomb | Einstein problem