science

Small stellapentakis dodecahedron

Small stellapentakis dodecahedron 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 stellapentakis dodecahedron rather than just read about it. In short: In geometry, the small stellapentakis dodecahedron is a nonconvex isohedral polyhedron. It is the dual of the truncated great dodecahedron.

Key takeaways

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

Reference excerpt

In geometry, the small stellapentakis dodecahedron is a nonconvex isohedral polyhedron. It is the dual of the truncated great dodecahedron. It has 60 intersecting triangular faces.

Proportions The triangles have two acute angles of arccos ⁡ ( 1 2 + 1 5 5 ) ≈ 18.699 407 085 149 ∘ {\displaystyle \arccos({\frac {1}{2}}+{\frac {1}{5}}{\sqrt {5}})\approx 18.699\,407\,085\,149^{\circ }} and one obtuse angle of arccos ⁡ ( 1 10 − 2 5 5 ) ≈ 142.601 185 829 70 ∘ {\displaystyle \arccos({\frac {1}{10}}-{\frac {2}{5}}{\sqrt {5}})\approx 142.601\,185\,829\,70^{\circ }} . The dihedral angle equals arccos ⁡ ( − 24 − 5 5 41 ) ≈ 149.099 125 827 35 ∘ {\displaystyle \arccos({\frac {-24-5{\sqrt {5}}}{41}})\approx 149.099\,125\,827\,35^{\circ }} . Part of each triangle lies within the solid, hence is invisible in solid models.

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

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

Illustrations

Worked examples

Example 1 — a first encounter with Small stellapentakis dodecahedron

Start with the simplest possible case. Write down what Small stellapentakis dodecahedron 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 stellapentakis dodecahedron 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 stellapentakis dodecahedron 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 stellapentakis dodecahedron

In research: Small stellapentakis dodecahedron 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 stellapentakis dodecahedron 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 stellapentakis dodecahedron is common in secondary-school and first-year university syllabi. It links to neighbouring topics Dual uniform polyhedra, Nonconvex polyhedra, Polyhedron stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Small stellapentakis dodecahedron 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 Small stellapentakis dodecahedron in 20 minutes

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

Frequently asked questions

What is Small stellapentakis dodecahedron in simple terms?

In geometry, the small stellapentakis dodecahedron is a nonconvex isohedral polyhedron. It is the dual of the truncated great dodecahedron.

Why does Small stellapentakis dodecahedron 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 stellapentakis dodecahedron?

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 stellapentakis dodecahedron.