Long Edge Of Deltoidal Icositetrahedron Given Total Surface Area Calculator

Formula Used:

\[ Long Edge = \sqrt{\frac{7 \times Total Surface Area}{12 \times \sqrt{61 + 38\sqrt{2}}}} \]

Long Edge of Deltoidal Icositetrahedron:

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1. What is the Long Edge of Deltoidal Icositetrahedron?

The Long Edge of Deltoidal Icositetrahedron is the length of the longest edge of the identical deltoidal faces of a Deltoidal Icositetrahedron. This geometric shape is a Catalan solid with 24 congruent deltoid faces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Long Edge = \sqrt{\frac{7 \times Total Surface Area}{12 \times \sqrt{61 + 38\sqrt{2}}}} \]

Where:

Total Surface Area — The total surface area of the Deltoidal Icositetrahedron in square meters (m²)

Explanation: This formula calculates the longest edge length based on the total surface area of the Deltoidal Icositetrahedron, using mathematical constants specific to this geometric shape.

3. Importance of Long Edge Calculation

Details: Calculating the long edge of a Deltoidal Icositetrahedron is important in geometry, crystallography, and architectural design where this specific polyhedron is used. It helps in understanding the proportions and dimensions of this complex geometric shape.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero. The calculator will compute the length of the longest edge of the Deltoidal Icositetrahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Icositetrahedron?
A: A Deltoidal Icositetrahedron is a Catalan solid with 24 congruent deltoid faces, 26 vertices, and 48 edges. It is the dual polyhedron of the rhombicuboctahedron.

Q2: What are the applications of this calculation?
A: This calculation is used in geometry research, architectural design, crystal structure analysis, and in creating mathematical models of complex polyhedra.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula is only applicable to the Deltoidal Icositetrahedron as it contains constants unique to this particular geometric shape.

Q4: What units should I use for the calculation?
A: The calculator uses meters for length and square meters for area. Ensure consistent units for accurate results.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise based on the formula. The accuracy of the result depends on the precision of the input value.