A STEM Project: Constructing Da Vinci's Divine Proportion Polyhedra Models - Part 2 of 2

Plate XXXI - Plate XXXVIII of Da Vinci's Polyhedra Models

Plate XL - Plate LIX of Da Vinci's Polyhedra Models

Leonardo Da Vinci drew fifty nine polyhedra models.  The first thirty were included in my last blog post https://www.blogger.com/blog/post/edit/5237417144570156489/3612955597216858264. The remaining twenty nine polyhedra models will be posted here.

Here is the PDF. I used 65lb. cardstock and vellum.

https://drive.google.com/file/d/1890TkEcAqpjCcOz6iGdXci5MvWYTMJyr/view?usp=sharing

Here is the .Studio file.

https://drive.google.com/file/d/1J63ZmmIp0L1IzCzyp53lUVwX3q2f-6JY/view?usp=sharing

Here is the SVG.

https://drive.google.com/file/d/1LCOpcfZrz63rGjsE4ulHXwRKXC7Oh8gk/view?usp=sharing

I duplicated Da Vinci's drawings by constructing three-dimensional paper models. In my description, I will give the side length measure and describe each model based on the number of faces, edges and vertices using Euler's formula.  For any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges.   Vertices + Faces - Edges = 2

A face is a flat, two-dimensional surface that serves as one side of a polyhedron.

An edge is a line segment where two faces meet.

Vertices is the plural of vertex.  Vertices are corner points which are formed by the intersection of faces.

Plate XXXI, XXXII - Solid & Hollow Elevated Dodecahedron aka Small Stellated Dodecahedron	Side Length of 1.618 inches
Faces	60 equilateral triangles
Edges	90
Vertices	32

Plate XXXI - Solid Elevated Dodecahedron

Plate XXXII -Hollow Elevated Dodecahedron

Plate XXXIII, XXXIV - Solid & Hollow Elevated  Truncated Dodecahedron	Side Length of 1.618 inches
Faces	120 equilateral triangles
Edges	180
Vertices	62

Plate XXXIII - Solid Elevated Truncated Dodecahedron

Plate XXXIV - Hollow Elevated Truncated Dodecahedron

Plate XXXV, XXXVI - Solid & Hollow Icosahexahedron aka Rhombicuboctahedron or Small Rhombic Cuboctahedron	Side Length of 1.618 inches
Faces	18 squares, 8 equilateral triangles
Edges	48
Vertices	24

Plate XXXV - Solid Icosahexahedron

Plate XXXVI - Hollow Icosahexahedron

Plate XXXVII, XXXVIII - Solid & Hollow Elevated Icosahexahedron aka Augmented Rhombicuboctahedron or Moravian Star	Side Length of 1.618 inches
Faces	96 equilateral triangles
Edges	144
Vertices	50

Plate XXXVII - Solid Elevated Icosahexahedron

Plate XXXVIII - Hollow Elevated Icosahexahedron

Plate XXXIX, XL - Solid & Hollow Septuagintaduarium Basium	Varying side lengths
Faces	24 isosceles triangles, 48 trapezoids
Edges	132
Vertices	62

Plate XXXIX - Solid Septuagintaduarium Basium

Plate XL - Hollow Septuagintaduarium Basium

Plate XLI, XLII  - Solid & Hollow Triangular Lateral Column	3.725 in. x 1.618 in.
Faces	2 equilateral triangles, 3 rectangles
Edges	9
Vertices	6

Plate XLI - Solid Lateral Triangular Column

Plate XLII - Hollow Lateral Triangular Column

Plate XLIII, XLIV  - Solid & Hollow Triangular Lateral Pyramid	3.725 in.height x 1.618 in.base
Faces	1 equilateral triangle, 3 isosceles triangles
Edges	6
Vertices	4

Plate XLIII - Solid Lateral Triangular Pyramid

Plate XLIV - Hollow Lateral Triangular Pyramid

Plate XLV, XLVI  - Solid & Hollow Quadrangular Lateral Column	3 in. x 1.618 in.
Faces	2 squares, 4 rectangles
Edges	12
Vertices	8

Plate XLV - Solid Quadrangular Lateral Column

Plate XLVI - Hollow Quadrangular Lateral Column

Plate XLVII, XLVIII  - Solid & Hollow Quadrangular Lateral Pyramid	3 in. X 1.618 in.
Faces	1 square, 4 isosceles triangles
Edges	8
Vertices	5

Plate XLVII - Solid Quadrangular Lateral Pyramid

Plate XLVIII - Hollow Quadrangular Lateral Pyramid

Plate XLIX, L - Solid & Hollow Pentagonal Lateral Column	4.3 in. x 1.618 in.
Faces	2 pentagons, 5 rectangles
Edges	15
Vertices	10

Plate XLIX - Solid Pentagonal Lateral Column

Plate L - Hollow Pentagonal Lateral Column

Plate LI, LIII- Solid & Hollow Pentagonal Lateral Pyramid	4.3 in. x 1.618 in.
Faces	1 pentagon, 5 isosceles triangles
Edges	10
Vertices	6

Plate LI - Solid Pentagonal Lateral Pyramid

Plate LII -Hollow Pentagonal Lateral Pyramid

Plate LIII, LIV - Solid & Hollow Hexagonal Lateral Column	5.2 in. x 1.618 in.
Faces	2 hexagons, 6 rectangles
Edges	18
Vertices	12

Plate LIII - Solid Hexagonal Lateral Column

Plate LIV - Hollow Hexagonal Lateral Column

Plate LIV, LV - Solid & Hollow Inequilateral Triangular Lateral Pyramid	Varying sizes
Faces	4 triangles
Edges	6
Vertices	4

Plate LV - Solid Inequilateral Triangular Lateral Pyramid

Plate LVI - Hollow Inequilateral Triangular Lateral Pyramid

Plate LVII - Solid Round Column	4.5 in. x 1.618 in.
Faces	2 circles
Edges	0
Vertices	0

Plate LVII - Solid Round Column

Plate LVIII - Solid Cone	4.5 in. x 1.618 in.
Faces	1 circle
Edges	0
Vertices	1

Plate LVIII - Solid Cone

Plate LVII - Solid Sphere	4.5 inch diameter
Faces	0
Edges	0
Vertices	0

Plate LIX - Solid Sphere - This sphere was made out of vellum paper because vellum is thinner and more flexible than cardstock.