Acronym | octatoe, oct || toe |
Name | (degenerate) octahedron atop truncated octahedron |
© | |
Segmentochoron display | |
Circumradius | ∞ i.e. flat in euclidean space |
Dihedral angles | |
Face vector | 30, 72, 58, 16 |
Confer |
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It either can be thought of as a degenerate 4D segmentotope with zero height, or as a 3D euclidean decomposition of the larger base into smaller bits.
Incidence matrix according to Dynkin symbol
xx3ox4oo&#x → height = 0 (oct || toe) o.3o.4o. | 6 * ♦ 4 4 0 0 | 4 4 4 0 0 | 1 4 1 0 .o3.o4.o | * 24 | 0 1 1 2 | 0 1 2 2 1 | 0 2 1 1 ------------+------+-------------+-------------+-------- x. .. .. | 2 0 | 12 * * * | 2 1 0 0 0 | 1 2 0 0 oo3oo4oo&#x | 1 1 | * 24 * * | 0 1 2 0 0 | 0 2 1 0 .x .. .. | 0 2 | * * 12 * | 0 1 0 2 0 | 0 2 0 1 .. .x .. | 0 2 | * * * 24 | 0 0 1 1 1 | 0 1 1 1 ------------+------+-------------+-------------+-------- x.3o. .. | 3 0 | 3 0 0 0 | 8 * * * * | 1 1 0 0 xx .. ..&#x | 2 2 | 1 2 1 0 | * 12 * * * | 0 2 0 0 .. ox ..&#x | 1 2 | 0 2 0 1 | * * 24 * * | 0 1 1 0 .x3.x .. | 0 6 | 0 0 3 3 | * * * 8 * | 0 1 0 1 .. .x4.o | 0 4 | 0 0 0 4 | * * * * 6 | 0 0 1 1 ------------+------+-------------+-------------+-------- x.3o.4o. ♦ 6 0 | 12 0 0 0 | 8 0 0 0 0 | 1 * * * xx3ox ..&#x ♦ 3 6 | 3 6 3 3 | 1 3 3 1 0 | * 8 * * .. ox4oo&#x ♦ 1 4 | 0 4 0 4 | 0 0 4 0 1 | * * 6 * .x3.x4.o ♦ 0 24 | 0 0 12 24 | 0 0 0 8 6 | * * * 1
ox3xx3ox&#x → height = 0 (oct || toe) o.3o.3o. | 6 * ♦ 4 4 0 0 0 | 2 2 2 4 2 0 0 0 | 1 2 1 2 0 .o3.o3.o | * 24 | 0 1 1 1 1 | 0 0 1 1 1 1 1 1 | 0 1 1 1 1 ------------+------+----------------+--------------------+---------- .. x. .. | 2 0 | 12 * * * * | 1 1 0 1 0 0 0 0 | 1 1 0 1 0 oo3oo3oo&#x | 1 1 | * 24 * * * | 0 0 1 1 1 0 0 0 | 0 1 1 1 0 .x .. .. | 0 2 | * * 12 * * | 0 0 1 0 0 1 1 0 | 0 1 1 0 1 .. .x .. | 0 2 | * * * 12 * | 0 0 0 1 0 1 0 1 | 0 1 0 1 1 .. .. .x | 0 2 | * * * * 12 | 0 0 0 0 1 0 1 1 | 0 0 1 1 1 ------------+------+----------------+--------------------+---------- o.3x. .. | 3 0 | 3 0 0 0 0 | 4 * * * * * * * | 1 1 0 0 0 .. x.3o. | 3 0 | 3 0 0 0 0 | * 4 * * * * * * | 1 0 0 1 0 ox .. ..&#x | 1 2 | 0 2 1 0 0 | * * 12 * * * * * | 0 1 1 0 0 .. xx ..&#x | 2 2 | 1 2 0 1 0 | * * * 12 * * * * | 0 1 0 1 0 .. .. ox&#x | 1 2 | 0 2 0 0 1 | * * * * 12 * * * | 0 0 1 1 0 .x3.x .. | 0 6 | 0 0 3 3 0 | * * * * * 4 * * | 0 1 0 0 1 .x .. .x | 0 4 | 0 0 2 0 2 | * * * * * * 6 * | 0 0 1 0 1 .. .x3.x | 0 6 | 0 0 0 3 3 | * * * * * * * 4 | 0 0 0 1 1 ------------+------+----------------+--------------------+---------- o.3x.3o. ♦ 6 0 | 12 0 0 0 0 | 4 4 0 0 0 0 0 0 | 1 * * * * ox3xx ..&#x ♦ 3 6 | 3 6 3 3 0 | 1 0 3 3 0 1 0 0 | * 4 * * * ox .. ox&#x ♦ 1 4 | 0 4 2 0 2 | 0 0 2 0 2 0 1 0 | * * 6 * * .. xx3ox&#x ♦ 3 6 | 3 6 0 3 3 | 0 1 0 3 3 0 0 1 | * * * 4 * .x3.x3.x ♦ 0 24 | 0 0 12 12 12 | 0 0 0 0 0 4 6 4 | * * * * 1
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