Charcoal, 162 146 bytes

Ｎθ⊞υ⟦⁰¦¹⊘⊕₂⁵⟧≔⟦⟧ηＦυＦＥ²⊞ＯΦιν×⊖⊗κ§ι⁰Ｆ¬№υκＦΦ⊞Ｏυκ⁼⁴ΣＸＥμ⁻ξ§κπ²⊞η⟦κμ⟧ＦηＦ…¹θ⊞υＥ§ι⁰⁺×κλ×⁻θꧧι¹μＦηＦΦυ⬤ι№η⟦μκ⟧Ｆ…²θＦ…¹λ⊞υＥ§ι⁰⁺⁺×μν×⁻λ짧ι¹ξ×⁻θλ§κξＩＥυ∕ι₂ΣＸι²

Try it online! Link is to verbose version of code. Explanation:

Ｎθ

Input b.

Ｎθ⊞υ⟦⁰¦¹⊘⊕₂⁵⟧≔⟦⟧ηＦυＦＥ²⊞ＯΦιν×⊖⊗κ§ι⁰Ｆ¬№υκＦΦ⊞Ｏυκ⁼⁴ΣＸＥμ⁻ξ§κπ²⊞η⟦κμ⟧

Generate the vertices and edges of a regular icosahedron of side 2.

ＦηＦ…¹θ⊞υＥ§ι⁰⁺×κλ×⁻θꧧι¹μ

Extrapolate the points along the edges.

ＦηＦΦυ⬤ι№η⟦μκ⟧Ｆ…²θＦ…¹λ⊞υＥ§ι⁰⁺⁺×μν×⁻λ짧ι¹ξ×⁻θλ§κξ

Extrapolate the points inside the faces. (Due to the normalisation, it's not necessary to interpolate.)

ＩＥυ∕ι₂ΣＸι²

Normalise all the points.