benchmarks.wiki / Public workspace
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Omni-MATH / Create a cube C₁ with edge length 1. Take the centers of the faces and connect them to form an octahedron O₁. Take the centers of the octahedron's faces and connect them to form a …
Problem
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problem
Create a cube with edge length 1. Take the centers of the faces and connect them to form an octahedron . Take the centers of the octahedron's faces and connect them to form a new cube . Continue this process infinitely. Find the sum of all the surface areas of the cubes and octahedrons.
Plain-text mathematical notation (without MathML)
Create a cube C₁ with edge length 1. Take the centers of the faces and connect them to form an octahedron O₁. Take the centers of the octahedron's faces and connect them to form a new cube C₂. Continue this process infinitely. Find the sum of all the surface areas of the cubes and octahedrons.
Original LaTeX notation
Create a cube $C_{1}$ with edge length 1. Take the centers of the faces and connect them to form an octahedron $O_{1}$. Take the centers of the octahedron's faces and connect them to form a new cube $C_{2}$. Continue this process infinitely. Find the sum of all the surface areas of the cubes and octahedrons.Discussion
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Source and history
- task_id
33af21a6-ac00-55e4-a829-bdfb567d5298- task_key
test--33af21a6-ac00-55e4-a829-bdfb567d5298- task_revision_id
- 1
- config / split
- / test
initial import