Pyramidal Edge Length of Triakis Icosahedron Given Total Surface Area Calculator

Formula Used:

\[ l_{pyramid} = \frac{15 - \sqrt{5}}{22} \times \sqrt{\frac{11 \times TSA}{15 \times \sqrt{109 - 30\sqrt{5}}}} \]

Pyramidal Edge Length:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Pyramidal Edge Length of Triakis Icosahedron?

The pyramidal edge length of a Triakis Icosahedron refers to the length of the edges forming the pyramids attached to each face of the underlying icosahedron. It is a key geometric parameter in understanding the structure and properties of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{pyramid} = \frac{15 - \sqrt{5}}{22} \times \sqrt{\frac{11 \times TSA}{15 \times \sqrt{109 - 30\sqrt{5}}}} \]

Where:

\( l_{pyramid} \) — Pyramidal edge length (m)
\( TSA \) — Total surface area of the Triakis Icosahedron (m²)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula derives the pyramidal edge length from the total surface area, incorporating the mathematical constants specific to the geometry of the Triakis Icosahedron.

3. Importance of Pyramidal Edge Length Calculation

Details: Calculating the pyramidal edge length is essential for geometric analysis, structural design, and understanding the spatial properties of the Triakis Icosahedron in various mathematical and engineering contexts.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive. The calculator will compute the corresponding pyramidal edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Icosahedron?
A: A Triakis Icosahedron is a Catalan solid that results from attaching a triangular pyramid to each face of a regular icosahedron.

Q2: Why is the formula so complex?
A: The complexity arises from the intricate geometry of the Triakis Icosahedron, which involves irrational numbers like √5 in its mathematical description.

Q3: What are typical values for pyramidal edge length?
A: The values depend on the size of the polyhedron. For a standard Triakis Icosahedron, the pyramidal edge length is proportional to the total surface area.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Triakis Icosahedron due to its unique geometric properties.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for an ideal Triakis Icosahedron, though real-world measurements may have practical limitations.