Geometry : Non-composite polyhedra with convex regular faces

Created on June 20, 2024.

/!\ THIS IS A WORK IN PROGRESS /!\

The goal is to gather all non-composite non-self-intersecting (convex and) non-convex regular-faced polyhedra. The convex ones are Zalgaller solids, this website explains it all.

Talk about the way to find them and which sections are complete (the ones in the table without a >)
+ spring model

viewer : have different colors per face + vertex/edge/face info like the gallery.

done: all the ones with v=4 to 11 + zalgaller
todo: what about ivanov q1-6 ? and stewart toroids ? v=12+ ? the ones fromSupermag + other sections ?

Each model view is interactive, the controls are the following:

  • Click and drag with the mouse right click to rotate the model.
  • Click and drag with the mouse left click to pan the model.
  • The mouse middle click zooms in or out.
  • Press R to reset the model position or triple click.
  • Press F to trigger fullscreen or double click.
  • Press P to pause/resume the animation.


# vertices 4 5 6 7 8 9 10 11 12 14 15 16 18 20
# polyhedra 1 1 2 0 3 5 10 18 >3 >2 >1 >2 >1 >2
# vertices 24 45 48 50 60 120
# polyhedra >4 >1 >1 >1 >5 >1

Tetrahedron
Square pyramid
Triangular Prism
Pentagonal Pyramid

None

Cube
Snub Disphenoid
Square Antiprism
Triangular Cupola
Tridiminished Icosahedron
9-trium
9-quadium
Pentagonal Prism
Pentagonal Antiprism
Sphenocorona
10-quadium
10-pentium
10-hexium
10-heptium
10-octium
10-ennium
10-unnilium
Mysterious Deltahedron
11-bium
11-trium
11-quadium
11-pentium
11-hexium
11-heptium
11-octium
11-ennium
11-unnilium
11-ununium
11-unbium
11-untrium
11-unquadium
11-unpentium
11-unhexium
11-heptium
11-unoctium
Square Cupola
Sphenomegacorona
Truncated Tetrahedron
Hebesphenomegacorona
Bilunabirotunda
Pentagonal Cupola
Snub Square Antiprism
Disphenocingulum
Triangular Hebesphenorotunda
Dodecahedron
Pentagonal Rotunda
Truncated Cube
Truncated Octahedron
R SnubCube
L SnubCube
Tridiminished Rhombicosidodecahedron
TruncatedCuboctahedron
Parabidiminished Rhombicosidodecahedron
Truncated Dodecahedron
Truncated Icosahedron
Rhombicosidodecahedron
R Snub Dodecahedron
L Snub Dodecahedron
Truncated Icosidodecahedron