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arXiv · 2603.00017

A Ten-Face Non-Edge-Sharing Wing Set on the Regular Icosahedron and a Decagonal Equatorial Balance

YoungJune Jeon
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Abstract

We formalize a ten-face triangular wing set on a regular icosahedron under a vertex labeling N, S, U1-U5, L1-L5 with rotation axis NS. The wing faces satisfy: (i) each face is an isosceles 36-36-108 triangle with a 36-degree angle anchored at a pole (N or S); (ii) distinct faces may share vertices but share no edges; and (iii) a natural equatorial cross-section yields a perfectly balanced regular decagon. We derive a closed form for the decagon radius, R = (phi/2)*ell, where ell is the icosahedron edge length and phi is the golden ratio phi = (1 + sqrt(5))/2. Beyond the geometric results, we interpret the ten-face closure as a symmetry-consistent design principle for a pole-anchored wing layout and provide a reproducible construction workflow.

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YoungJune Jeon. 2026-02-02. A Ten-Face Non-Edge-Sharing Wing Set on the Regular Icosahedron and a Decagonal Equatorial Balance. https://arxiv.org/abs/2603.00017

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