mathematics

Gyroelongated pyramid

Gyroelongated pyramid is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Gyroelongated pyramid rather than just read about it. In short: In geometry, the gyroelongated pyramids (also called augmented antiprisms) are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal antiprism. There are two gyroelongated pyramids that are Johnson solids made from regular triangles, square, and pentagons.

Key takeaways

Gyroelongated pyramid belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Gyroelongated pyramid to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Gyroelongated pyramid from memory before moving on to harder problems.

Reference excerpt

In geometry, the gyroelongated pyramids (also called augmented antiprisms) are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal antiprism. There are two gyroelongated pyramids that are Johnson solids made from regular triangles, square, and pentagons. A triangular and hexagonal form can be constructed with coplanar faces. Others can be constructed allowing for isosceles triangles.

Forms

See also Gyroelongated bipyramid Elongated bipyramid Elongated pyramid Diminished trapezohedron

References

Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others. Victor A. Zalgaller (1969). Convex Polyhedra with Regular Faces. Consultants Bureau. No ISBN. The first proof that there are only 92 Johnson solids.

Illustrations

Worked examples

Example 1 — a first encounter with Gyroelongated pyramid

Start with the simplest possible case. Write down what Gyroelongated pyramid claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Gyroelongated pyramid before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Gyroelongated pyramid ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Gyroelongated pyramid

In research: Gyroelongated pyramid appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Gyroelongated pyramid in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Gyroelongated pyramid is common in secondary-school and first-year university syllabi. It links to neighbouring topics Polyhedron stubs, Pyramids (geometry), so understanding it makes those chapters shorter.
In everyday life: Look for Gyroelongated pyramid outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Gyroelongated pyramid in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Gyroelongated pyramid means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Gyroelongated pyramid out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Gyroelongated pyramid in simple terms?

Why does Gyroelongated pyramid matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Gyroelongated pyramid?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Gyroelongated pyramid.