All of the models included in my collection (or models created by others equivalent to them).

Platonic solids
Tetrahedron	Cube	Octahedron	Dodecahedron	Icosahedron

Kepler–Poinsot polyhedra
Great dodecahedron	Small stellated dodecahedron	Great icosahedron	Great stellated dodecahedron

Archimedean solids
Truncated tetrahedron	Cuboctahedron	Truncated cube	Truncated octahedron	Rhombicuboctahedron
Truncated cuboctahedron	Snub cuboctahedron	Icosidodecahedron	Truncated dodecahedron	Truncated icosahedron
Rhombicosidodeca-hedron	Truncated icosidodecahedron	Snub icosidodecahedron

Catalan solids
Triakis tetrahedron	Rhombic dodecahedron	Triakis octahedron	Tetrakis cube	Deltoidal icositetrahedron
Disdyakis dodecahedron	Pentagonal icositetrahedron	Rhombic triacontahedron	Triakis icosahedron	Pentakis dodecahedron
Deltoidal hexecontahedron	Disdyakis triacontahedron	Pentagonal hexecontahedron

Uniform star polyhedra
Octahemioctahedron	Tetrahemicube	Small cubicuboctahedron	Great cubicuboctahedron	Cubohemioctahedron
Cubitruncated cuboctahedron	Nonconvex great rhombicuboctahedron	Small rhombicube	Stellated truncated cube	Great truncated cuboctahedron
Great rhombicube	Small ditrigonal icosidodecahedron	Small icosicosidodecahedron	Small snub icosicosidodecahedron	Small dodecicosidodeca-hedron
Dodecadodecahedron	Truncated great dodecahedron	Rhombidodecadodeca-hedron	Small rhombidodecahedron	Snub dodecadodecahedron
Ditrigonal dodecadodecahedron	Small ditrigonal dodecicosidodeca-hedron	Great ditrigonal dodecicosidodeca-hedron	Icosidodecadodeca-hedron	Icositruncated dodecadodecahedron
Snub icosidodecadodeca-hedron	Great ditrigonal icosidodecahedron	Great icosicosidodecahedron	Small icosihemidodecahedron	Small dodecicosahedron
Small dodecahemidodeca-hedron	Great icosidodecahedron	Truncated great icosahedron	Rhombicosahedron	Great snub icosidodecahedron
Small stellated truncated dodecahedron	Truncated dodecadodecahedron	Inverted snub dodecadodecahedron	Great dodecicosidodeca-hedron	Small dodecahemicosahedron
Great dodecicosahedron	Great snub dodecicosidodeca-hedron	Great dodecahemicosahedron	Great stellated truncated dodecahedron	Nonconvex great rhombicosidodeca-hedron
Great truncated icosidodecahedron	Great inverted snub icosidodecahedron	Great dodecahemidodeca-hedron	Great icosihemidodecahedron	Small retrosnub icosicosidodecahedron
Great rhombidodecahedron	Great retrosnub icosidodecahedron	Great dirhombicosidodeca-hedron	Great disnub dirhombidodecahedron

Dual uniform star polyhedra
[TBA] Octahemioctacron	[TBA] Tetrahemihexacron	Small hexacronic icositetrahedron	Great hexacronic icositetrahedron	[TBA] Cubohemioctacron
Tetradyakis cube	Great deltoidal icositetrahedron	Small rhombihexacron	Great triakis octahedron	Great disdyakis dodecahedron
Great rhombihexacron	Small triambic icosahedron	Small icosacronic hexecontahedron	Small hexagonal hexecontahedron	Small dodecacronic hexecontahedron
Medial rhombic triacontahedron	Small stellapentakis dodecahedron	Medial deltoidal hexecontahedron	Small rhombidodecacron	Medial pentagonal hexecontahedron
Medial triambic icosahedron	Small ditrigonal dodecacronic hexecontahedron	Great ditrigonal dodecacronic hexecontahedron	Medial icosacronic hexecontahedron	Tridyakis icosahedron
Medial hexagonal hexecontahedron	Great triambic icosahedron	Great icosacronic hexecontahedron	[TBA] Small icosihemidodecacron	Small dodecicosacron
[TBA] Small dodecahemidodecacron	Great rhombic triacontahedron	Great stellapentakis dodecahedron	Rhombicosacron	Great pentagonal hexecontahedron
Great pentakis dodecahedron	Medial disdyakis triacontahedron	Medial inverted pentagonal hexecontahedron	Great dodecacronic hexecontahedron	[TBA] Small dodecahemicosacron
Great dodecicosacron	Great hexagonal hexecontahedron	[TBA] Great dodecahemicosacron	Great triakis icosahedron	Great deltoidal hexecontahedron
Great disdyakis triacontahedron	Great inverted pentagonal hexecontahedron	[TBA] Great dodecahemidodecacron	[TBA] Great icosihemidodecacron	Small hexagrammic hexecontahedron
Great rhombidodecacron	Great pentagrammic hexecontahedron	[TBA] Great dirhombicosidodecacron	[TBA] Great disnub dirhombidodecacron

Prisms
Triangular prism	Square prism	Pentagonal prism	Pentagrammic prism	Hexagonal prism
Heptagonal prism	Heptagrammic prism	Great heptagrammic prism	Octagonal prism	Octagrammic prism
Enneagonal prism	Enneagrammic prism	Great enneagrammic prism	Decagonal prism	Decagrammic prism
Hendecagonal prism	Small hendecagrammic prism	Hendecagrammic prism	Great hendecagrammic prism	Grand hendecagrammic prism
Dodecagonal prism	Dodecagrammic prism

Bipyramids (dual uniform)
Triangular bipyramid	Square bipyramid	Pentagonal bipyramid	Pentagrammic bipyramid	Hexagonal bipyramid
Heptagonal bipyramid	Heptagrammic bipyramid	Great heptagrammic bipyramid	Octagonal bipyramid	Octagrammic bipyramid
Enneagonal bipyramid	Enneagrammic bipyramid	Great enneagrammic bipyramid	Decagonal bipyramid	Decagrammic bipyramid
Hendecagonal bipyramid	Small hendecagrammic bipyramid	Hendecagrammic bipyramid	Great hendecagrammic bipyramid	Grand hendecagrammic bipyramid
Dodecagonal bipyramid	Dodecagrammic bipyramid

Bipyramids (regular faces)
Triangular bipyramid	Square bipyramid	Pentagonal bipyramid	Pentagrammic bipyramid	Hexagonal bipyramid
Heptagrammic bipyramid	Great heptagrammic bipyramid	Octagrammic bipyramid	Enneagrammic bipyramid	Great enneagrammic bipyramid
Decagrammic bipyramid	Small hendecagrammic bipyramid	Hendecagrammic bipyramid	Great hendecagrammic bipyramid	Grand hendecagrammic bipyramid
Dodecagrammic bipyramid

Antiprisms
Triangular antiprism	Square antiprism	Pentagonal antiprism	Pentagrammic antiprism	Hexagonal antiprism
Heptagonal antiprism	Heptagrammic antiprism	Great heptagrammic antiprism	Octagonal antiprism	Octagrammic antiprism
Enneagonal antiprism	Enneagrammic antiprism	Great enneagrammic antiprism	Decagonal antiprism	Decagrammic antiprism
Hendecagonal antiprism	Small hendecagrammic antiprism	Hendecagrammic antiprism	Great hendecagrammic antiprism	Grand hendecagrammic antiprism
Dodecagonal antiprism	Dodecagrammic antiprism

Trapezohedra
Triangular trapezohedron	Square trapezohedron	Pentagonal trapezohedron	Pentagrammic trapezohedron	Hexagonal trapezohedron
Heptagonal trapezohedron	Heptagrammic trapezohedron	Great heptagrammic trapezohedron	Octagonal trapezohedron	Octagrammic trapezohedron
Enneagonal trapezohedron	Enneagrammic trapezohedron	Great enneagrammic trapezohedron	Decagonal trapezohedron	Decagrammic trapezohedron
Hendecagonal trapezohedron	Small hendecagrammic trapezohedron	Hendecagrammic trapezohedron	Great hendecagrammic trapezohedron	Grand hendecagrammic trapezohedron
Dodecagonal trapezohedron	Dodecagrammic trapezohedron

Cupolas and cuploids
Triangular cupola	Crossed triangular cuploid	Square cupola	Crossed square cupola	Pentagonal cupola
Pentagrammic cuploid	Crossed pentagrammic cupola	Crossed pentagonal cuploid	Hexagonal cupola	Crossed hexagonal cupola
Heptagrammic cuploid	Great heptagrammic cupola	Crossed great heptagrammic cuploid	Crossed heptagrammic cupola	Octagrammic cupola
Crossed octagrammic cupola	Enneagrammic cuploid	Great enneagrammic cuploid	Crossed great enneagrammic cupola	Crossed enneagrammic cupola
Decagrammic cupola	Crossed decagrammic cupola	Small hendecagrammic cuploid	Hendecagrammic cupola	Great hendecagrammic cuploid
Grand hendecagrammic cupola	Crossed grand hendecagrammic cuploid	Crossed great hendecagrammic cupola	Crossed hendecagrammic cuploid	Crossed small hendecagrammic cupola
Dodecagrammic cupola	Crossed dodecagrammic cupola

Trapezopyramids and keratinoids
[TBA] Triangular trapezopyramid	[TBA] Crossed triangular keratinoid	Square trapezopyramid	Crossed square trapezopyramid	Pentagonal trapezopyramid
Pentagrammic keratinoid	Crossed pentagrammic trapezopyramid	Crossed pentagonal keratinoid	Hexagonal trapezopyramid	Crossed hexagonal trapezopyramid
Heptagrammic keratinoid	Great heptagrammic trapezopyramid	Crossed great heptagrammic keratinoid	Crossed heptagrammic trapezopyramid	Octagrammic trapezopyramid
Crossed octagrammic trapezopyramid	Enneagrammic keratinoid	Great enneagrammic keratinoid	Crossed great enneagrammic trapezopyramid	Crossed enneagrammic trapezopyramid
Decagrammic trapezopyramid	Crossed decagrammic trapezopyramid	Small hendecagrammic keratinoid	Hendecagrammic trapezopyramid	Great hendecagrammic keratinoid
Grand hendecagrammic trapezopyramid	Crossed grand hendecagrammic keratinoid	Crossed great hendecagrammic trapezopyramid	Crossed hendecagrammic keratinoid	Crossed small hendecagrammic trapezopyramid
Dodecagrammic trapezopyramid	Crossed dodecagrammic trapezopyramid