Stellated truncated hexahedron
Encyclopedia
In geometry
, the stellated truncated hexahedron (or quasitruncated hexahedron) is a uniform star polyhedron, indexed as U19. It is represented by Schläfli symbol t0,1{4/3,3}, and Coxeter-Dynkin diagram
, . It is sometimes called quasitruncated hexahedron because it is related to the truncated cube
, , except that the square faces become inverted into {8/3} octagrams.
Note that stellated truncated hexahedron is not a true stellation
of the truncated hexahedron; its convex 'core' is nonuniform.
with three other uniform polyhedra
: the convex rhombicuboctahedron
, the small rhombihexahedron
, and the small cubicuboctahedron
.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the stellated truncated hexahedron (or quasitruncated hexahedron) is a uniform star polyhedron, indexed as U19. It is represented by Schläfli symbol t0,1{4/3,3}, and Coxeter-Dynkin diagram
Coxeter-Dynkin diagram
In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors...
, . It is sometimes called quasitruncated hexahedron because it is related to the truncated cube
Truncated cube
In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces , 36 edges, and 24 vertices....
, , except that the square faces become inverted into {8/3} octagrams.
Note that stellated truncated hexahedron is not a true stellation
Stellation
Stellation is a process of constructing new polygons , new polyhedra in three dimensions, or, in general, new polytopes in n dimensions. The process consists of extending elements such as edges or face planes, usually in a symmetrical way, until they meet each other again...
of the truncated hexahedron; its convex 'core' is nonuniform.
Related polyhedra
It shares the vertex arrangementVertex arrangement
In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes....
with three other uniform polyhedra
Uniform polyhedron
A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive...
: the convex rhombicuboctahedron
Rhombicuboctahedron
In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. There are 24 identical vertices, with one triangle and three squares meeting at each. Note that six of the squares only share vertices with the triangles...
, the small rhombihexahedron
Small rhombihexahedron
In geometry, the small rhombihexahedron is a nonconvex uniform polyhedron, indexed as U18. It has 18 faces , 48 edges, and 24 vertices. Its vertex figure is an antiparallelogram.-Related polyhedra:...
, and the small cubicuboctahedron
Small cubicuboctahedron
In geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13. It has 20 faces , 48 edges, and 24 vertices. Its vertex figure is a crossed quadrilateral.- Related polyhedra :...
.
 Rhombicuboctahedron Rhombicuboctahedron In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. There are 24 identical vertices, with one triangle and three squares meeting at each. Note that six of the squares only share vertices with the triangles... |
 Small cubicuboctahedron Small cubicuboctahedron In geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13. It has 20 faces , 48 edges, and 24 vertices. Its vertex figure is a crossed quadrilateral.- Related polyhedra :... |
 Small rhombihexahedron Small rhombihexahedron In geometry, the small rhombihexahedron is a nonconvex uniform polyhedron, indexed as U18. It has 18 faces , 48 edges, and 24 vertices. Its vertex figure is an antiparallelogram.-Related polyhedra:... |
 Stellated truncated hexahedron |