science

Small rhombidodecacron

Small rhombidodecacron 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 Small rhombidodecacron rather than just read about it. In short: In geometry, the small rhombidodecacron is a nonconvex isohedral polyhedron. It is the dual of the small rhombidodecahedron.

Key takeaways

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

Reference excerpt

In geometry, the small rhombidodecacron is a nonconvex isohedral polyhedron. It is the dual of the small rhombidodecahedron. It is visually identical to the Small dodecacronic hexecontahedron. It has 60 intersecting antiparallelogram faces.

Proportions Each face has two angles of arccos ⁡ ( 5 8 + 1 8 5 ) ≈ 25.242 832 961 52 ∘ {\displaystyle \arccos({\frac {5}{8}}+{\frac {1}{8}}{\sqrt {5}})\approx 25.242\,832\,961\,52^{\circ }} and two angles of arccos ⁡ ( − 1 2 + 1 5 5 ) ≈ 93.025 844 508 96 ∘ {\displaystyle \arccos(-{\frac {1}{2}}+{\frac {1}{5}}{\sqrt {5}})\approx 93.025\,844\,508\,96^{\circ }} . The diagonals of each antiparallelogram intersect at an angle of arccos ⁡ ( 1 4 + 1 10 5 ) ≈ 61.731 322 529 52 ∘ {\displaystyle \arccos({\frac {1}{4}}+{\frac {1}{10}}{\sqrt {5}})\approx 61.731\,322\,529\,52^{\circ }} . The ratio between the lengths of the long edges and the short ones equals 1 2 + 1 2 5 {\displaystyle {\frac {1}{2}}+{\frac {1}{2}}{\sqrt {5}}} , which is the golden ratio. The dihedral angle equals arccos ⁡ ( − 19 − 8 5 41 ) ≈ 154.121 363 125 78 ∘ {\displaystyle \arccos({\frac {-19-8{\sqrt {5}}}{41}})\approx 154.121\,363\,125\,78^{\circ }} .

References Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208

External links Weisstein, Eric W. "Small rhombidodecacron". MathWorld. Uniform polyhedra and duals

Illustrations

Worked examples

Example 1 — a first encounter with Small rhombidodecacron

Start with the simplest possible case. Write down what Small rhombidodecacron 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 Small rhombidodecacron 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 Small rhombidodecacron 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 Small rhombidodecacron

In research: Small rhombidodecacron 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 Small rhombidodecacron 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: Small rhombidodecacron is common in secondary-school and first-year university syllabi. It links to neighbouring topics Dual uniform polyhedra, Polyhedron stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Small rhombidodecacron 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 “Small rhombidodecacron” →

Affiliate

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

How to study Small rhombidodecacron in 20 minutes

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

Frequently asked questions

What is Small rhombidodecacron in simple terms?

In geometry, the small rhombidodecacron is a nonconvex isohedral polyhedron. It is the dual of the small rhombidodecahedron.

Why does Small rhombidodecacron 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 Small rhombidodecacron?

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 Small rhombidodecacron.