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(last updated on 25.03.2026)

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Archimedean Solids in the Fifteenth and Sixteenth Centuries

Daniele Barbaro

• chapter XVI: rectified truncated octahedron
• chapter XVIII: rectified truncated icosahedron
• chapter XIX: truncated pentakis dodecahedron
• chapter XX: twice-truncated icosahedron
• chapter XXII: twice-truncated octahedron
• chapter XXV: truncated rectified truncated octahedron
• chapter XXXIV: elongated truncated octahedron
• chapter XXXIV: chamfered cube
• chapter XXXIV: no name yet
• chapter XXXIV: truncated rectified truncated icosahedron

geometry projects

studying

• Euclid’s Elements
  • book XII, proposition 17
• symmetries
  • transitivity of the pentagonal dodecahedron
• art and math seminar at KSU
• tessellations @ IASS2021

modelling

• the convex regular:
  • tetrahedron
  • octahedron
  • icosahedron
  • hexahedron
  • dodecahedron
• the convex quasiregular:
  • cuboctahedron, CO
  • icosidodecahedron, ID
• the convex semiregular:
  • truncated tetrahedron, tT
  • truncated octahedron, tO
  • truncated cube, tC

3d models

• of the concave regular
  • stellated dodecahedra
• of the concave quasiregular:
  • great dodecadodecahedron
  • great icosidodecahedron
  • small ditrigonal icosidodecahedron
  • great ditrigonal icosidodecahedron
  • ditrigonal dodecadodecahedron
  • tetrahemihexahedron
  • octahemioctahedron
  • cubohemioctahedron
  • small icosihemidodecahedron
  • small dodecahemidodecahedron
  • great dodecahemicosahedron
  • small dodecahemicosahedron
  • great dodecahemidodecahedron
  • great icosihemidodecahedron
• of the concave semiregular
  • great icosicosidodecahedron
• of dual pairs
  • great stellated triacontahedron | great icosidodecahedron

enclosing

• inside the regular tetrahedron
  • tetrahedron inside the tetrahedron
  • octahedron inside the tetrahedron
  • icosahedron inside the tetrahedron
  • cube inside the tetrahedron
  • dodecahedron inside the tetrahedron
  • the Archimedeans inside the tetrahedron
• inside the regular octahedron
  • regular facets of the octahedron
  • tetrahedra inside the octahedron
  • icosahedron inside the octahedron
  • cube inside the octahedron 01
  • cubes inside the octahedron 02
  • dodecahedron inside the octahedron
• inside the regular icosahedron
  • regular facets of the icosahedron
  • tetrahedra inside the icosahedron
  • octahedra inside the icosahedron
  • cubes inside the icosahedron
  • dodecahedron inside the icosahedron
  • small stellated dodecahedron inside the icosahedron
  • great dodecahedron inside the icosahedron
  • great icosahedron inside the icosahedron
• inside the cube
  • regular facets of the cube
  • tetrahedra inside the cube
  • octahedron inside the cube 01
  • octahedra inside the cube 02
  • icosahedra inside the cube
  • dodecahedra inside the cube 01
  • dodecahedron from the cube 02
• inside the regular dodecahedron
  • regular facets of the dodecahedron
  • tetrahedra inside the dodecahedron
  • octahedra inside the dodecahedron
  • icosahedron inside the dodecahedron
  • cubes inside the dodecahedron
  • great stellated dodecahedron inside the dodecahedron

expanding

• expanding the edges (e₁)
  • expansion of the edges of regular polygons
  • expansion of the edges of regular polygons of density 2
  • expansion of the edges of the convex regular polyhedra
• expanding the faces (e₂)
  • snubbing the cube onto the cuboctahedron

chamfering

• chamfering the convex regular polyhedra
  • chamfering the cube

tessellating

• in 2D
• in 3D
  • tessellating with truncated octahedra

interlocking

plane geometry

• theorems
  • Napoleon’s theorem
• plane polygons
  • triangles
  • quadrangles
  • regular pentagon
  • regular hexagon
  • regular octagon
  • regular decagon
• plane curves
  • curves
  • conics

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