Convexes and non-convexes

How to Close/Open

Select the viewing mode here:

In each element of the list below you can

  • see an image of the polyhedron by pressing the image at the left
  • if a net is available
    • see an image of the net by pressing the image at the right
    • see an animation of the conversion of the polyhedron to the net by pressing the arrow from left to right
    • see an animation of the reverse conversion (from the net to the polyhedron) by pressing the arrow from right to left
  • see and manipulate the polyhedron by pressing the icon at the upper left corner
    • in desktops, rotate with the mouse left-button, zoom with the mouse wheel, go fullscreen with the F11 key
    • in mobile devices, rotate with a finger, zoom by pinching in or out
  • In stereo mode with no glasses or with prisms, toggle between the parallel and the cross-eyed viewing methods with the x key

The imagery available here were prepared using Mathematica and Three.js.

The interactive applications included here were carried out under a grant from FCT - Fundação para a Ciência e a Tecnologia.








Truncated tetrahedron


Truncated octahedron

Truncated cube

Small rhombicuboctahedron

Great rhombicuboctahedron

Snub cube


Truncated icosahedron

Truncated dodecahedron

Small rhombicosidodecahedron

Great rhombicosidodecahedron

Snub dodecahedron

Triakis tetrahedron

Rhombic dodecahedron

Tetrakis hexahedron

Small triakis octahedron

Deltoidal icositetrahedron

Disdyakis dodecahedron

Pentagonal icositetrahedron

Rhombic triacontahedron

Pentakis dodecahedron

Triakis icosahedron

Deltoidal hexecontahedron

Disdyakis triacontahedron

Pentagonal hexecontahedron

Square pyramid (J1)

Pentagonal pyramid (J2)

Triangular cupola (J3)

Square cupola (J4)

Pentagonal cupola (J5)

Pentagonal rotunda (J6)

Elongated triangular pyramid (J7)

Elongated square pyramid (J8)

Elongated pentagonal pyramid (J9)

Gyroelongated square pyramid (J10)

Gyroelongated pentagonal pyramid (J11)

Triangular dipyramid (J12)

Pentagonal dipyramid (J13)

Elongated triangular dipyramid (J14)

Elongated square dipyramid (J15)

Elongated pentagonal dipyramid (J16)

Gyroelongated square dipyramid (J17)

Elongated triangular cupola (J18)

Elongated square cupola (J19)

Elongated pentagonal cupola (J20)

Elongated pentagonal rotunda (J21)

Gyroelongated triangular cupola (J22)

Gyroelongated square cupola (J23)

Gyroelongated pentagonal cupola (J24)

Gyroelongated pentagonal rotunda (J25)

Gyrobifastigium (J26)

Triangular orthobicupola (J27)

Square orthobicupola (J28)

Square gyrobicupola (J29)

Pentagonal orthobicupola (J30)

Pentagonal gyrobicupola (J31)

Pentagonal orthocupolarotunda (J32)

Pentagonal gyrocupolarotunda (J33)

Pentagonal orthobirotunda (J34)

Elongated triangular orthobicupola (J35)

Elongated triangular gyrobicupola (J36)

Elongated square gyrobicupola (J37)

Elongated pentagonal orthobicupola (J38)

Elongated pentagonal gyrobicupola (J39)

Elongated pent. orthocupolarotunda (J40)

Elongated pentag. gyrocupolarotunda (J41)

Elongated pentagonal orthobirotunda (J42)

Elongated pentagonal gyrobirotunda (J43)

Gyroelongated triangular bicupola (J44)

Gyroelongated square bicupola (J45)

Gyroelongated pentagonal bicupola (J46)

Gyroelongated pentag. cupolarotunda (J47)

Gyroelongated pentag. birotunda (J48)

Augmented triangular prism (J49)

Biaugmented triangular prism (J50)

Triaugmented triangular prism (J51)

Augmented pentagonal prism (J52)

Biaugmented pentagonal prism (J53)

Augmented hexagonal prism (J54)

Parabiaugmented hexagonal prism (J55)

Metabiaugmented hexagonal prism (J56)

Triaugmented hexagonal prism J57)

Augmented Dodecahedron (J58)

Parabiaugmented dodecahedron (J59)

Metabiaugmented dodecahedron (J60)

Triaugmented dodecahedron (J61)

Metabidiminished icosahedron (J62)

Tridiminished icosahedron (J63)

Augmented tridiminished icosahedron (J64)

Augmented truncated tetrahedron (J65)

Augmented truncated cube (J66)

Biaugmented truncated cube (J67)

Augmented truncated dodecahedron (J68)

Parabiaugmented trunc. dodecahedron (J69)

Metabiaugmented trunc. dodecahedron (J70)

Triaugmented truncated dodecahedron (J71)

Gyrate rhombicosidodeca. (J72)

Parabigyrate rhombicosidodeca.(J73)

Metabigyrate rhombicosidodeca. (J74)

Trigyrate rhombicosidodeca. (J75)

Diminished rhombicosidodeca. (J76)

Paragyrate dim. rhombicosidodeca. (J77)

Metagyrate dim. rhombicosidodeca. (J78)

Bigyrate dimin. rhombicosidodeca. (J79)

Parabidiminished rhombicosidodeca. (J80)

Metabidiminished rhombicosidodeca. (J81)

Gyrate bidim. rhombicosidodeca. (J82)

Tridiminished rhombicosidodeca. (J83)

Snub disphenoid (J84)

Snub square antiprism (J85)

Sphenocorona (J86)

Augmented sphenocorona (J87)

Sphenomegacorona (J88)

Hebesphenomegacorona (J89)

Disphenocingulum (J90)

Bilunabirotunda (J91)

Triangular hebesphenorotunda (J92)

Acute golden rhombohedron

Obtuse golden rhombohedron

Triangular prism

Pentagonal prism

Hexagonal prism

Heptagonal prism

Octagonal prism

Nonagonal prism

Decagonal prism

Square Antiprism

Pentagonal Antiprism

Hexagonal Antiprism

Heptagonal Antiprism

Octagonal Antiprism

Nonagonal Antiprism

Decagonal Antiprism

Dürer solid

Elongated dodecahedron

Squashed dodecahedron

Rhombic icosahedron

Rhombic enneacontahedron



Stella octangula

Tetrahedron 2-compound

Tetrahedron 3-compound

Cube 2-compound

Cube-octahedron compound

First tetrahedron 4-compound

Second tetrahedron 4-compound

Third tetrahedron 4-compound

Cube 3-compound

Tetrahedron 5-compound

Tetrahedron 6-compound

First cube 4-compound

Second cube 4-compound

Dodecahedron 2-compound

Octahedron 3-compound

Cube 5-compound

First octahedron 4-compound

Second octahedron 4-compound

Dodecahedron-icosahedron compound

Cube 6-compound

Icosahedron 2-compound

Octahedron 5-compound

Tetrahedron 10-compound

Cube-octahedron 3-compound

Pentagonal prism 6-compound

Cube 10-compound

Dodecahedron 5-compound

Cube-octahedron 5-compound

Dodecahedron 6-compound

Octahedron 10-compound

Icosahedron 5-compound

Icosahedron 6-compound

Small stellated dodecahedron

Great Dodecahedron

Great stellated dodecahedron

Great Icosahedron

Szilassi polyhedron

Cumulated tetrahedron

Császár polyhedron

Jessen′s orthogonal icosahedron

Cumulated cube

Escher solid

Third rhombic dodecahedron stellation

Cumulated dodecahedron

Rhombic hexecontahedron

Small triambic icosahedron

Cumulated icosahedron

Second rhombic dodecahedron stellation

Dodeca-small triambic icosahedron comp.


Great rhombic triacontahedron