science

Gyroelongated square cupola

Gyroelongated square cupola is a science 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 square cupola rather than just read about it. In short: In geometry, the gyroelongated square cupola is one of the Johnson solids (J23). As the name suggests, it can be constructed by gyroelongating a square cupola (J4) by attaching an octagonal antiprism to its base.

Key takeaways

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

Reference excerpt

In geometry, the gyroelongated square cupola is one of the Johnson solids (J23). As the name suggests, it can be constructed by gyroelongating a square cupola (J4) by attaching an octagonal antiprism to its base. It can also be seen as a gyroelongated square bicupola (J45) with one square bicupola removed. A Johnson solid is one of 92 strictly convex polyhedra that are 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.

Area and volume The surface area is

A = ( 7 + 2 2 + 5 3 ) a 2 ≈ 18.4886811... a 2 . {\displaystyle A=\left(7+2{\sqrt {2}}+5{\sqrt {3}}\right)a^{2}\approx 18.4886811...a^{2}.}

The volume is the sum of the volume of a square cupola and the volume of an octagonal prism,

V = ( 1 + 2 3 2 + 2 3 4 + 2 2 + 2 146 + 103 2 ) a 3 {\displaystyle V=\left(1+{\frac {2}{3}}{\sqrt {2}}+{\frac {2}{3}}{\sqrt {4+2{\sqrt {2}}+2{\sqrt {146+103{\sqrt {2}}}}}}\right)a^{3}} ≈ 6.2107658... a 3 . {\displaystyle \approx 6.2107658...a^{3}.}

Dual polyhedron The dual of the gyroelongated square cupola has 20 faces: 8 kites, 4 rhombi, and 8 pentagons.

References

External links Weisstein, Eric W., "Gyroelongated square cupola" ("Johnson solid") at MathWorld.

Illustrations

Worked examples

Example 1 — a first encounter with Gyroelongated square cupola

Start with the simplest possible case. Write down what Gyroelongated square cupola claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 square cupola 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 square cupola 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 square cupola

In research: Gyroelongated square cupola appears in science 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 square cupola 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 square cupola is common in secondary-school and first-year university syllabi. It links to neighbouring topics Johnson solids, Polyhedron stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Gyroelongated square cupola 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 square cupola in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Gyroelongated square cupola 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 square cupola out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Gyroelongated square cupola in simple terms?

Why does Gyroelongated square cupola matter?

Because it connects several science 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 square cupola?

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 square cupola.