why does the amount of regular shapes go from infinity to like 5 when making the jump from 2d to 3d
The internal angles at any given vertex have to be less than 360 degrees (or else the shape is flat). Also at any given vertex, 3 or more faces are meeting. So the only combinations of 3+ regular polygons that have additive internal angles of less than 360 degrees are: 3 triangles (60×3), aka, Te…
The Short Answer
The internal angles at any given vertex have to be less than 360 degrees (or else the shape is flat). Also at any given vertex, 3 or more faces are meeting. So the only combinations of 3+ regular polygons that have additive internal angles of less than 360 degrees are: 3 triangles (60×3), aka, Tetrahedron 4 triangles (60×4), aka, Octahedron 5 triangles (60×5), aka, Icosahedron 3 Squares (90×3), aka, Cube and 3 Pentagons (108×3), aka, Dodecahedron You can't use shapes bigger than Pentagons because 3 hexagons would be 120×3=360=flat
Analysis
Key Concepts: Triangles, internal, angles
This explanation focuses on triangles, internal, angles and spans 80 words across 3 sentences. The depth is typical for History questions (category average: 72 words), striking a balance between accessibility and completeness.
What This Answer Covers
The explanation opens with: “The internal angles at any given vertex have to be less than 360 degrees (or else the shape is flat).” It then elaborates by explaining the root cause, ultimately building toward a complete picture across 3 connected points.
How This Compares in History
Ranked #188 of 500 History questions by answer depth (top 38%). This falls in the detailed tier — above average depth. The explanation goes beyond surface-level but keeps things accessible.
Frequently Asked Questions
Is there a simple explanation for why the amount of regular shapes go from infinity to like 5 when making the jump from 2d to 3d?
The internal angles at any given vertex have to be less than 360 degrees (or else the shape is flat). Also at any given vertex, 3 or more faces are meeting. So the only combinations of 3+ regular polygons that have additive internal angles of less…
How detailed is this explanation compared to similar History questions?
This is an above-average answer at 80 words, ranked #188 of 500 History questions by depth. The key concepts covered are triangles, internal, angles.
What approach does this answer take to explain the amount of regular shapes go from infinity to like 5 when?
The explanation uses root cause analysis across 80 words. It is categorized under History and addresses the question through 1 analytical lens.