science

Small icosihemidodecahedron

Small icosihemidodecahedron 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 icosihemidodecahedron rather than just read about it. In short: In geometry, the small icosihemidodecahedron (or small icosahemidodecahedron) is a uniform star polyhedron, indexed as U49. It has 26 faces (20 triangles and 6 decagons), 60 edges, and 30 vertices.

Key takeaways

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

Reference excerpt

In geometry, the small icosihemidodecahedron (or small icosahemidodecahedron) is a uniform star polyhedron, indexed as U49. It has 26 faces (20 triangles and 6 decagons), 60 edges, and 30 vertices. Its vertex figure alternates two regular triangles and decagons as a crossed quadrilateral. It is a hemipolyhedron with its six decagonal faces passing through the model center. It is given a Wythoff symbol, 3⁄2 3 | 5, but that construction represents a double covering of this model.

Related polyhedra It shares its edge arrangement with the icosidodecahedron (its convex hull, having the triangular faces in common), and with the small dodecahemidodecahedron (having the decagonal faces in common).

See also Pentakis icosidodecahedron List of uniform polyhedra

References

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

Illustrations

Worked examples

Example 1 — a first encounter with Small icosihemidodecahedron

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

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

Affiliate

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

How to study Small icosihemidodecahedron in 20 minutes

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

Frequently asked questions

What is Small icosihemidodecahedron in simple terms?

In geometry, the small icosihemidodecahedron (or small icosahemidodecahedron) is a uniform star polyhedron, indexed as U49. It has 26 faces (20 triangles and 6 decagons), 60 edges, and 30 vertices.

Why does Small icosihemidodecahedron 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 icosihemidodecahedron?

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 icosihemidodecahedron.