Acronym | ... |
Name | tetra-augmented axially-octahedral ursachoron xoBo3ofox3xooo&#xt |
© | |
Circumradius | ... |
Coordinates |
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Face vector | 28, 102, 118, 44 |
Confer |
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It shall be noted here that just this alternating tetra-augmentation remains convex. Neighbouring teddies well can be augmented, but neither the dihedral angle at the pentagon then would remain convex (as for tetu), nor the cavity could be bridged by further unit edges (as for the iku).
Incidence matrix according to Dynkin symbol
xoBo3ofox3xooo&#xt (for heights and B cf. the coords) (co || pseudo f-oct || pseudo B-tet || oct) o...3o...3o... | 12 * * * | 2 2 2 1 0 0 0 0 | 1 2 1 2 1 2 2 2 0 0 0 0 | 1 1 2 1 1 2 0 0 .o..3.o..3.o.. | * 6 * * | 0 0 4 0 2 1 0 0 | 0 0 0 2 4 2 0 4 2 0 0 0 | 0 2 1 0 4 2 0 0 ..o.3..o.3..o. | * * 4 * ♦ 0 0 0 3 3 0 3 0 | 0 0 0 0 0 0 3 6 3 3 0 0 | 0 0 0 1 3 3 1 0 ...o3...o3...o | * * * 6 | 0 0 0 0 0 1 2 4 | 0 0 0 0 4 0 0 0 2 4 2 2 | 0 2 0 0 4 0 2 1 -------------------+----------+------------------------+--------------------------------+------------------ x... .... .... | 2 0 0 0 | 12 * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0 .... .... x... | 2 0 0 0 | * 12 * * * * * * | 0 1 1 0 0 1 1 0 0 0 0 0 | 1 0 1 1 0 1 0 0 oo..3oo..3oo..&#x | 1 1 0 0 | * * 24 * * * * * | 0 0 0 1 1 1 0 1 0 0 0 0 | 0 1 1 0 1 1 0 0 o.o.3o.o.3o.o.&#x | 1 0 1 0 | * * * 12 * * * * | 0 0 0 0 0 0 2 2 0 0 0 0 | 0 0 0 1 1 2 0 0 .oo.3.oo.3.oo.&#x | 0 1 1 0 | * * * * 12 * * * | 0 0 0 0 0 0 0 2 1 0 0 0 | 0 0 0 0 2 1 0 0 .o.o3.o.o3.o.o&#x | 0 1 0 1 | * * * * * 6 * * | 0 0 0 0 4 0 0 0 2 0 0 0 | 0 2 0 0 4 0 0 0 ..oo3..oo3..oo&#x | 0 0 1 1 | * * * * * * 12 * | 0 0 0 0 0 0 0 0 1 2 0 0 | 0 0 0 0 2 0 1 0 .... ...x .... | 0 0 0 2 | * * * * * * * 12 | 0 0 0 0 1 0 0 0 0 1 1 1 | 0 1 0 0 1 0 1 1 -------------------+----------+------------------------+--------------------------------+------------------ x...3o... .... | 3 0 0 0 | 3 0 0 0 0 0 0 0 | 4 * * * * * * * * * * * | 1 1 0 0 0 0 0 0 x... .... x... | 4 0 0 0 | 2 2 0 0 0 0 0 0 | * 6 * * * * * * * * * * | 1 0 1 0 0 0 0 0 .... o...3x... | 3 0 0 0 | 0 3 0 0 0 0 0 0 | * * 4 * * * * * * * * * | 1 0 0 0 0 0 0 0 xo.. .... ....&#x | 2 1 0 0 | 1 0 2 0 0 0 0 0 | * * * 12 * * * * * * * * | 0 1 1 0 0 0 0 0 .... of.x ....&#xt | 1 2 0 2 | 0 0 2 0 0 2 0 1 | * * * * 12 * * * * * * * | 0 1 0 0 1 0 0 0 .... .... xo..&#x | 2 1 0 0 | 0 1 2 0 0 0 0 0 | * * * * * 12 * * * * * * | 0 0 1 0 0 1 0 0 .... .... x.o.&#x | 2 0 1 0 | 0 1 0 2 0 0 0 0 | * * * * * * 12 * * * * * | 0 0 0 1 0 1 0 0 ooo.3ooo.3ooo.&#x | 1 1 1 0 | 0 0 1 1 1 0 0 0 | * * * * * * * 24 * * * * | 0 0 0 0 1 1 0 0 .ooo3.ooo3.ooo&#x | 0 1 1 1 | 0 0 0 0 1 1 1 0 | * * * * * * * * 12 * * * | 0 0 0 0 2 0 0 0 .... ..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 0 2 1 | * * * * * * * * * 12 * * | 0 0 0 0 1 0 1 0 ...o3...x .... | 0 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * * * * 4 * | 0 1 0 0 0 0 0 1 .... ...x3...o | 0 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * * * * * 4 | 0 0 0 0 0 0 1 1 -------------------+----------+------------------------+--------------------------------+------------------ x...3o...3x... ♦ 12 0 0 0 | 12 12 0 0 0 0 0 0 | 4 6 4 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * xo.o3of.x ....&#xt ♦ 3 3 0 3 | 3 0 6 0 0 3 0 3 | 1 0 0 3 3 0 0 0 0 0 1 0 | * 4 * * * * * * xo.. .... xo..&#x ♦ 4 1 0 0 | 2 2 4 0 0 0 0 0 | 0 1 0 2 0 2 0 0 0 0 0 0 | * * 6 * * * * * .... o.o.3x.o.&#x ♦ 3 0 1 0 | 0 3 0 3 0 0 0 0 | 0 0 1 0 0 0 3 0 0 0 0 0 | * * * 4 * * * * .... ofox ....&#xr ♦ 1 2 1 2 | 0 0 2 1 2 2 2 1 | 0 0 0 0 1 0 0 2 2 1 0 0 | * * * * 12 * * * cycle: (ABDC) .... .... xoo.&#x ♦ 2 1 1 0 | 0 1 2 2 1 0 0 0 | 0 0 0 0 0 1 1 2 0 0 0 0 | * * * * * 12 * * .... ..ox3..oo&#x ♦ 0 0 1 3 | 0 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 3 0 1 | * * * * * * 4 * ...o3...x3...o ♦ 0 0 0 6 | 0 0 0 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * * 1
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