Johnson Solids

Besides the regular and semiregular solids, there are just ninety-two other convex polyhedra with regular faces. In 1966, the American mathematician Norman W. Johnson, a student of H.S.M. Coxeter at the University of Toronto in Canada, enumerated them. These polyhedra are sometimes called the Johnson solids. In 1969, the Russian Viktor A. Zalgaller offered a computer-based computational proof that Johnson had completed the enumeration of convex polyhedra with regular faces.

This pyramid has a square base and four equilateral triangles on the sides.For further information about Berman's models of regular-faced convex polyhedra, see 1978.1065.01.Currently not on view
Description
This pyramid has a square base and four equilateral triangles on the sides.
For further information about Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.021
accession number
1978.1065
catalog number
1978.1065.021
This pyramid has a regular pentagon for its base and five equilateral triangles on the sides.For further information about Berman's models of regular-faced convex polyhedra, see 1978.1065.01.Currently not on view
Description
This pyramid has a regular pentagon for its base and five equilateral triangles on the sides.
For further information about Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.022
accession number
1978.1065
catalog number
1978.1065.022
This model has a regular hexagon on the base, an equilateral triangle on top, and three squares and three equilateral triangles around the sides.
Description
This model has a regular hexagon on the base, an equilateral triangle on top, and three squares and three equilateral triangles around the sides. TIn sum, the faces are four equilateral triangles, three squares, and one regular hexagon.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.023
accession number
1978.1065
catalog number
1978.1065.023
This model has a square top, an octagonal base, and four squares and four equilateral triangles around the sides.For further information about Berman's models of regular-faced convex polyhedra, see 1978.1065.01.Currently not on view
Description
This model has a square top, an octagonal base, and four squares and four equilateral triangles around the sides.
For further information about Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.024
accession number
1978.1065
catalog number
1978.1065.024
The top face of this model is a pentagon, the bottom a regular decagon. Around the sides are five squares and five equilateral triangles, alternating.On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.Currently not on view
Description
The top face of this model is a pentagon, the bottom a regular decagon. Around the sides are five squares and five equilateral triangles, alternating.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.025
accession number
1978.1065
catalog number
1978.1065.025
This model has a regular pentagon on the top, and a regular decagon on the bottom. There are ten equilateral triangles and five regular pentagons around the sides.
Description
This model has a regular pentagon on the top, and a regular decagon on the bottom. There are ten equilateral triangles and five regular pentagons around the sides. Hence the faces are ten equilateral triangles, six regular pentagons, and one regular decagon.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.026
accession number
1978.1065
catalog number
1978.1065.026
The model has three squares faces around a triangular base. Three equilateral triangles rise from the other end to meet at a vertex.
Description
The model has three squares faces around a triangular base. Three equilateral triangles rise from the other end to meet at a vertex. Hence the total number of faces is four equilateral triangles and three squares.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.027
accession number
1978.1065
catalog number
1978.1065.027
This model resembles a cube with a square pyramid on one face. The faces are five square faces and four equilateral triangles.On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.Currently not on view
Description
This model resembles a cube with a square pyramid on one face. The faces are five square faces and four equilateral triangles.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.028
accession number
1978.1065
catalog number
1978.1065.028
The base of this model is a pentagon, with five squares rising from it. The top is a pyramid with five triangular sides.
Description
The base of this model is a pentagon, with five squares rising from it. The top is a pyramid with five triangular sides. Hence the faces of the pyramid are a regular pentagon, five squares, and five equilateral triangles.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.029
accession number
1978.1065
catalog number
1978.1065.029
This model has a square base, eight triangular sides, and four triangles arranged in a pyramid at the top. The faces thus are twelve equilateral triangles and one square.On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.Currently not on view
Description
This model has a square base, eight triangular sides, and four triangles arranged in a pyramid at the top. The faces thus are twelve equilateral triangles and one square.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.030
accession number
1978.1065
catalog number
1978.1065.030
This model has a regular pentagon for a base, ten equilateral triangles that form the sides, and five equilateral triangles arranged in a pyramid at the top.
Description
This model has a regular pentagon for a base, ten equilateral triangles that form the sides, and five equilateral triangles arranged in a pyramid at the top. Hence the faces are fifteen equilateral triangles and one regular pentagon.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.031
accession number
1978.1065
catalog number
1978.1065.031
This model has six equilateral triangles for faces, arranged like two regular tetrahedra facing in opposite directions.On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.Currently not on view
Description
This model has six equilateral triangles for faces, arranged like two regular tetrahedra facing in opposite directions.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.032
accession number
1978.1065
catalog number
1978.1065.032
The faces of this model are ten equilateral triangles, arranged like two pentagonal pyramids on the same base.On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.Currently not on view
Description
The faces of this model are ten equilateral triangles, arranged like two pentagonal pyramids on the same base.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.033
accession number
1978.1065
catalog number
1978.1065.033
This model resembles a triangular pyramid with a regular tetrahedron on each end. Its faces are three squares and six equilateral triangles.On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.Currently not on view
Description
This model resembles a triangular pyramid with a regular tetrahedron on each end. Its faces are three squares and six equilateral triangles.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.034
accession number
1978.1065
catalog number
1978.1065.034
This model resembles a cube with square pyramids on two opposite ends.Its faces are four squares, and eight equilateral triangles.On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.Currently not on view
Description
This model resembles a cube with square pyramids on two opposite ends.Its faces are four squares, and eight equilateral triangles.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.035
accession number
1978.1065
catalog number
1978.1065.035
The faces of model include five squares arranged as in the sides of a prism, with pentagonal pyramids of five equilateral triangles each rising from both ends.
Description
The faces of model include five squares arranged as in the sides of a prism, with pentagonal pyramids of five equilateral triangles each rising from both ends. Its faces total ten equilateral triangles and five squares.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.036
accession number
1978.1065
catalog number
1978.1065.036
The faces of this model are sixteen equilateral triangles. Four are arranged in pyramid on one end, four in a pyramid at the bottom, and the remainder around the middle as in an antiprism.On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.Currently not on view
Description
The faces of this model are sixteen equilateral triangles. Four are arranged in pyramid on one end, four in a pyramid at the bottom, and the remainder around the middle as in an antiprism.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.037
accession number
1978.1065
catalog number
1978.1065.037
This model has an equilateral triangle on the top and a regular hexagon on the bottom. Six squares rise from the hexagon. Three squares and three equilateral triangles are above these.
Description
This model has an equilateral triangle on the top and a regular hexagon on the bottom. Six squares rise from the hexagon. Three squares and three equilateral triangles are above these. The model has a total of four equilateral triangles, nine squares, and one regular hexagon for faces.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.038
accession number
1978.1065
catalog number
1978.1065.038
This model has a square top, four squares and four equilateral triangles in next layer, eight squares in next layer, and a regular octagon on bottom.
Description
This model has a square top, four squares and four equilateral triangles in next layer, eight squares in next layer, and a regular octagon on bottom. Thus its faces total four equilateral triangles, thirteen squares, and one regular octagon.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.039
accession number
1978.1065
catalog number
1978.1065.039
This model has a regular pentagon on top, a round of five squares and five equilateral triangles, a round of ten squares, and a regular decagon on the bottom.
Description
This model has a regular pentagon on top, a round of five squares and five equilateral triangles, a round of ten squares, and a regular decagon on the bottom. It has a total of five triangular faces, fifteen square faces, one pentagonal face and one decagonal face.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.040
accession number
1978.1065
catalog number
1978.1065.040
This model has a regular pentagon on the top, a round of five equilateral triangles, a round of five regular pentagons and five equilateral triangles, a round of ten squares, and a regular decagon on the bottom.
Description
This model has a regular pentagon on the top, a round of five equilateral triangles, a round of five regular pentagons and five equilateral triangles, a round of ten squares, and a regular decagon on the bottom. Hence its faces total of six regular pentagons, ten equilateral triangles, ten squares, and a regular decagon.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.041
accession number
1978.1065
catalog number
1978.1065.041
The top of this model is an equilateral triangle and the bottom a regular hexagon. Above the hexagon is a ring of twelve equilateral triangles in alternating directions. Above these triangles is a row of three equilateral triangles alternating with three squares.
Description
The top of this model is an equilateral triangle and the bottom a regular hexagon. Above the hexagon is a ring of twelve equilateral triangles in alternating directions. Above these triangles is a row of three equilateral triangles alternating with three squares. The model has a total of sixteen equilateral triangles, three squares, and one regular hexagon.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.042
accession number
1978.1065
catalog number
1978.1065.042
The base of this model is a regular octagon, the top a square. Above the octagon is a round of sixteen equilateral triangles, alternating in orientation. Above the triangles is a round of four squares and four triangles.
Description
The base of this model is a regular octagon, the top a square. Above the octagon is a round of sixteen equilateral triangles, alternating in orientation. Above the triangles is a round of four squares and four triangles. The model has a total of twenty equilateral triangles, four squares, and one regular octagon.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.043
accession number
1978.1065
catalog number
1978.1065.043
The bottom of this model is a regular decagon, the top a regular pentagon. Above the decagon are twenty triangular faces. Above these are five squares which alternate with five triangles.
Description
The bottom of this model is a regular decagon, the top a regular pentagon. Above the decagon are twenty triangular faces. Above these are five squares which alternate with five triangles. Hence the faces are twenty-five equilateral triangles, five squares, one regular pentagon, and one regular decagonal.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.
Location
Currently not on view
date made
1970
maker
Berman, Martin
ID Number
1978.1065.044
accession number
1978.1065
catalog number
1978.1065.044

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