Uniform Polyhedra, including Skilling's figure, including links to 'molecular' files of all the uniform Polyhedra.

Johnson Solids: All remaining convex polyhedra with regular faces.

Noble Polyhedra: Connor Hill's complete set of polyhedra which are both face and vertex transitive. NEW 2026

Acrohedra: Polyhedra with a specified vertex, n-n-3 acrons, n-4-3-3 acrons, n-6-3 acrons, n-6-4 acrons, some near misses (with 'Stress Maps') and tables of dihedral angles.

Rectangular and Crossed-Rectangular Polyhedra: UPDATED 2026   Isohedra containing rectangular or crossed-rectangular faces.

Toroids:  

• Szilassi and Császár polyhedra, 
• some of the simpler Stewart Toroids 
• a focus on the "K4-World",
• the "T5-Country" and
  
• Flying Further into the "K5-Galaxy"   NEW 2024
• Toroids formed from augmented duals of uniform polyhedra  
• Canonical Toroids

Rhombohedra: Polyhedra containing rhombic faces:

• Isohedral Rhombohedra  
• Convex Rhombic Polyhedra with Icosahedral Symmetry   
• Convex Polyhedra containing Rhombi as found in the Rhombic Dodecahedron    
• Convex Polyhedra containing Golden Rhombi    
• Variations on a Rhombic Theme (non convex isomorphs to the above)  
  
• Monorhombal Edge Rhombified Polyhedra NEW 2025
• The Rhombic Enneacontahedron and partial zonohedrifications of the Dodecahedron   
• The Great Rhombic Enneacontahedron   
• Bi-Rhombic Polyhedra with Icosahedral Symmetry   
• Dissecting the Expanded Rhombic Dodecahedron  
• Dissecting the Rhombic Triacontahedron  
• Rhombified Stellations of Snub Uniform Polyhedra,
• Rhombically Expanded Deltahedra  
• Cupolaic Expanded Rhombohedra and
• Molybi Augmented Polyhedra  
  

Arruated Polyhedra:   NEW 2025  Augmenting the Platonic and Archimedean polyhedra with sets of triangular wedges to create new forms.

Triangulated Archimedean Polyhedra:   NEW 2026  Exploring polyhedra generated by replacing octagonal and decagonal faces with triangular pyramids, and beyond.

N-gonal Substituted Polyhedra:  NEW 2025  A structured search for heptagonal variants of the Platonic and Archimedean polyhedra.   

Isohedral Deltahedra:  Face transitive polyhedra consisting of equilateral triangles.  

Elementary Honeycombs: Vertex transitive space filling honeycombs with non-uniform cells.

Petrie Expanded Polyhedra:  Polyhedra that have been expanded across their Petrie Polygons 

Convex Segmentochora: Dr Richard Klitzing's models of 4-dimensional figures confined to two hyper-planes.  Includes VRML models of all figures. 

Polyhedral 'Twisters': Animations of an unusual deformation between uniform polyhedra.  

Tessellations of the Plane: Uniform polygonal tessellations of the plane and hyperbolic star tessellations. 

Locally convex octahedral and icosahedral polyhedra: Locally convex polyhedra with high degrees of symmetry.

Locally Convex Prismatic Polyhedra: Commentary and models of 

• snub anti-prisms: an infinite family of 2-regular prismatic polyhedra  
• bi-snub anti-prisms: an infinite family of 3-regular prismatic polyhedra
• spheno-prisms: an infinite family of prismatic polyhedra based on the sphenoid
• elongated spheno-prisms: the above family can be elongated by the insertion of square faces
• gyro-elongated spheno-prisms: the sphenoprisms can also be gyro-elongated, a disphenocingulum is among the results
• 'pentaprisms':  relatives of the dodecahedron with the pentagons augmented by pyramids.
• n-4-3-3 polyhedra: a family of prismatic polyhedra containing n-4-3-3 vertices  

Chiral Prismatic Polyhedra:   Commentary and models of 

• tetrakis snub prisms: adding pyramids to the faces of a snub cube results in an infinite family of polyhedra 
• pentakis snub pentaprisms: the same happens when pyramids are added to the faces of a snub dodecahedron 
• cingulated anti-prisms: possibly the simplest family of chiral prismatic polyhedra
• see also n-4-3-3 polyhedra above
  

Cupolas and Semicupolas: Polyhedra based on the cupola with emphasis on the great rhombicosidodecahedron and the ditrigonary polyhedra.

• self augmented heptagonal semicupola   

Sphenocoronal Polyhedra: Families of prismatic polyhedra based on the 

• sphenocorona, 
• sphenomegacorona and 
• hebesphenomegacorona.

Isomorphs of the Icosahedron:  Polyhedra generated from an icosahedral net. 

Isomorphs of the Rhombicuboctahedron: Polyhedra generated from a rhombicuboctahedral net, with animated VRMLs. 

Phi in the Icosahedron and Dodecahedron:  A simple method of generating vertex co-ordinates using the Golden Ratio  

Miscellaneous Polyhedra: Including models of the Stewart G3, the self augmented heptagonal antiprism the Edshammar polyhedron and the associahedron 

Near Misses:  Polyhedra that are not quite regular, including near-misses to the Johnson Solids (the 'A-list') and acrohedral near misses amongst others. 

Polyhedral Links

Update Timeline
 

NEW 2026

Jim McNeill