science

Pentagonal orthobicupola

Pentagonal orthobicupola 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 Pentagonal orthobicupola rather than just read about it. In short: In geometry, the pentagonal orthobicupola is one of the Johnson solids (J30). As the name suggests, it can be constructed by joining two pentagonal cupolae (J5) along their decagonal bases, matching like faces.

Key takeaways

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

Reference excerpt

In geometry, the pentagonal orthobicupola is one of the Johnson solids (J30). As the name suggests, it can be constructed by joining two pentagonal cupolae (J5) along their decagonal bases, matching like faces. A 36-degree rotation of one cupola before the joining yields a pentagonal gyrobicupola (J31). The pentagonal orthobicupola is the third in an infinite set of orthobicupolae. 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 ( 5 + 4 5 ) a 3 ≈ 4.64809... a 3 {\displaystyle V={\frac {1}{3}}\left(5+4{\sqrt {5}}\right)a^{3}\approx 4.64809...a^{3}}

A = ( 10 + 5 2 ( 10 + 5 + 75 + 30 5 ) ) a 2 ≈ 17.7711... a 2 {\displaystyle A=\left(10+{\sqrt {{\frac {5}{2}}\left(10+{\sqrt {5}}+{\sqrt {75+30{\sqrt {5}}}}\right)}}\right)a^{2}\approx 17.7711...a^{2}}

References

External links Weisstein, Eric W., "Pentagonal orthobicupola" ("Johnson solid") at MathWorld.

Illustrations

Worked examples

Example 1 — a first encounter with Pentagonal orthobicupola

Start with the simplest possible case. Write down what Pentagonal orthobicupola 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 Pentagonal orthobicupola 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 Pentagonal orthobicupola 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 Pentagonal orthobicupola

In research: Pentagonal orthobicupola 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 Pentagonal orthobicupola 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: Pentagonal orthobicupola 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 Pentagonal orthobicupola 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 Pentagonal orthobicupola in 20 minutes

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

Frequently asked questions

What is Pentagonal orthobicupola in simple terms?

Why does Pentagonal orthobicupola 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 Pentagonal orthobicupola?

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 Pentagonal orthobicupola.