Rectified 9-cubes

In nine-dimensional geometry, a rectified 9-cube is a convex uniform 9-polytope, being a rectification of the regular 9-cube.

9-orthoplex	Rectified 9-orthoplex	Birectified 9-orthoplex
Trirectified 9-orthoplex	Quadrirectified 9-cube	Trirectified 9-cube
Birectified 9-cube	Rectified 9-cube	9-cube
Orthogonal projections in BC9 Coxeter plane

There are 9 rectifications of the 9-cube. The zeroth is the 9-cube itself, and the 8th is the dual 9-orthoplex. Vertices of the rectified 9-cube are located at the edge-centers of the 9-orthoplex. Vertices of the birectified 9-cube are located in the square face centers of the 9-cube. Vertices of the trirectified 9-orthoplex are located in the cube cell centers of the 9-cube. Vertices of the quadrirectified 9-cube are located in the tesseract centers of the 9-cube.

These polytopes are part of a family 511 uniform 9-polytopes with BC₉ symmetry.

Rectified 9-cube

Alternate names

• Rectified enneract (Acronym ren) (Jonathan Bowers)^[1]

Images

orthographic projections

B9		B8		B7
[18]		[16]		[14]
B6			B5
[12]			[10]
B4		B3		B2
[8]		[6]		[4]
A7		A5		A3
—		—		—
[8]		[6]		[4]

Birectified 9-cube

Alternate names

• Birectified enneract (Acronym barn) (Jonathan Bowers)^[2]

Images

orthographic projections

B9		B8		B7
[18]		[16]		[14]
B6			B5
[12]			[10]
B4		B3		B2
[8]		[6]		[4]
A7		A5		A3
—		—		—
[8]		[6]		[4]

Trirectified 9-cube

Alternate names

• Trirectified enneract (Acronym tarn) (Jonathan Bowers)^[3]

Images

orthographic projections

B9		B8		B7
[18]		[16]		[14]
B6			B5
[12]			[10]
B4		B3		B2
[8]		[6]		[4]
A7		A5		A3
—		—		—
[8]		[6]		[4]

Quadrirectified 9-cube

Alternate names

• Quadrirectified enneract (Acronym nav) (Jonathan Bowers)^[4]

Images

orthographic projections

B9		B8		B7
[18]		[16]		[14]
B6			B5
[12]			[10]
B4		B3		B2
[8]		[6]		[4]
A7		A5		A3
—		—		—
[8]		[6]		[4]