Midsphere Radius Of Deltoidal Icositetrahedron Given Total Surface Area Calculator

Formula Used:

\[ r_m = \frac{1+\sqrt{2}}{2} \times \sqrt{\frac{7 \times TSA}{12 \times \sqrt{61+38\sqrt{2}}}} \]

Midsphere Radius (rₘ):

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1. What is the Midsphere Radius of Deltoidal Icositetrahedron?

The Midsphere Radius of a Deltoidal Icositetrahedron is the radius of the sphere that is tangent to all the edges of the Deltoidal Icositetrahedron. It represents the sphere that fits perfectly within the polyhedron, touching each edge at exactly one point.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_m = \frac{1+\sqrt{2}}{2} \times \sqrt{\frac{7 \times TSA}{12 \times \sqrt{61+38\sqrt{2}}}} \]

Where:

\( r_m \) — Midsphere Radius (m)
\( TSA \) — Total Surface Area of the Deltoidal Icositetrahedron (m²)

Explanation: This formula calculates the midsphere radius based on the total surface area of the deltoidal icositetrahedron, using the mathematical relationship between these two geometric properties.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and 3D modeling as it helps understand the spatial properties of the deltoidal icositetrahedron, which is useful in various applications including crystallography, architecture, and mathematical research.

4. Using the Calculator

Tips: Enter the total surface area of the deltoidal icositetrahedron in square meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Icositetrahedron?
A: A Deltoidal Icositetrahedron is a Catalan solid with 24 deltoid (kite-shaped) faces. It is the dual polyhedron of the rhombicuboctahedron.

Q2: What units should I use for the input?
A: The calculator expects the total surface area in square meters (m²). If your measurement is in different units, convert it to square meters first.

Q3: Can this calculator handle very large or very small values?
A: Yes, the calculator can process a wide range of values as long as they are positive numbers greater than zero.

Q4: How accurate is the calculation?
A: The calculation uses PHP's built-in mathematical functions which provide high precision. The result is rounded to 4 decimal places for readability.

Q5: What if I get an error message?
A: Make sure you've entered a valid positive number for the total surface area and that the value is greater than zero.