science

Gyroelongated triangular cupola

Gyroelongated triangular 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 triangular cupola rather than just read about it. In short: In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J22). It can be constructed by attaching a hexagonal antiprism to the base of a triangular cupola (J3).

Key takeaways

Gyroelongated triangular 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 triangular cupola to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Gyroelongated triangular cupola from memory before moving on to harder problems.

Reference excerpt

In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J22). It can be constructed by attaching a hexagonal antiprism to the base of a triangular cupola (J3). This is called "gyroelongation", which means that an antiprism is joined to the base of a solid, or between the bases of more than one solid. The gyroelongated triangular cupola can also be seen as a gyroelongated triangular bicupola (J44) with one triangular cupola removed. Like all cupolae, the base polygon has twice as many sides as the top (in this case, the bottom polygon is a hexagon because the top is a triangle). 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.

Formulae The following formulae for volume and surface area can be used if all faces are regular, with edge length a:

V = ( 1 3 61 2 + 18 3 + 30 1 + 3 ) a 3 ≈ 3.51605... a 3 {\displaystyle V=\left({\frac {1}{3}}{\sqrt {{\frac {61}{2}}+18{\sqrt {3}}+30{\sqrt {1+{\sqrt {3}}}}}}\right)a^{3}\approx 3.51605...a^{3}}

A = ( 3 + 11 3 2 ) a 2 ≈ 12.5263... a 2 {\displaystyle A=\left(3+{\frac {11{\sqrt {3}}}{2}}\right)a^{2}\approx 12.5263...a^{2}}

Dual polyhedron The dual of the gyroelongated triangular cupola has 15 faces: 6 kites, 3 rhombi, and 6 pentagons.

References

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

Illustrations

Worked examples

Example 1 — a first encounter with Gyroelongated triangular cupola

Start with the simplest possible case. Write down what Gyroelongated triangular 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 triangular 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 triangular 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 triangular cupola

In research: Gyroelongated triangular 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 triangular 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 triangular 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 triangular 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Gyroelongated triangular cupola” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Gyroelongated triangular cupola in 20 minutes

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

Frequently asked questions

What is Gyroelongated triangular cupola in simple terms?

In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J22). It can be constructed by attaching a hexagonal antiprism to the base of a triangular cupola (J3).

Why does Gyroelongated triangular 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 triangular 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 triangular cupola.