| Acronym | ... |
| Name | truncation of icoap |
| Circumradius | sqrt[19+9 sqrt(2)]/2 = 2.816377 |
| Face vector | 672, 2640, 3744, 2064, 290 |
| Confer |
It is quite remarkable that icoap allows for some of the same operations as regulars do: this polyteron is nothing but the truncation operation being applied to it.
Incidence matrix according to symbol extension
trunc( xo3oo4oo3ox&#x ) trops( x. .. .. .. ) & | 384 * | 1 0 3 3 0 | 3 3 3 6 0 3 | 3 6 3 1 3 0 3 1 | 1 3 4 1 trops( oo3oo4oo3oo&#x ) | * 288 | 0 1 0 4 4 | 0 2 0 4 4 8 | 0 8 8 0 1 1 4 4 | 0 2 8 1 --------------------------+---------+----------------------+---------------------------+------------------------------+------------ trunc( x. .. .. .. ) & | 2 0 | 192 * * * * | 3 3 0 0 0 0 | 3 6 3 0 0 0 0 0 | 1 3 4 0 trunc( oo3oo4oo3oo&#x ) | 0 2 | * 144 * * * ♦ 0 8 0 0 0 0 | 0 8 8 0 0 0 0 0 | 0 2 8 0 verf( x.3o. .. .. ) & | 2 0 | * * 576 * * | 1 0 2 2 0 0 | 2 2 0 1 2 0 1 0 | 1 2 1 1 verfA( xo .. .. ..&#x ) & | 1 1 | * * * 1152 * | 0 1 0 2 0 2 | 0 2 2 0 1 0 2 1 | 0 1 3 1 verfB( xo .. .. ..&#x ) & | 0 2 | * * * * 576 | 0 1 0 0 2 2 | 0 2 2 0 0 1 1 2 | 0 1 3 1 --------------------------+---------+----------------------+---------------------------+------------------------------+------------ trunc( x.3o. .. .. ) & | 6 0 | 3 0 3 0 0 | 192 * * * * * | 2 2 0 0 0 0 0 0 | 1 2 1 0 trunc( xo .. .. ..&#x ) & | 2 4 | 1 2 0 2 1 | * 576 * * * * | 0 2 2 0 0 0 0 0 | 0 1 3 0 verf( x.3o.4o. .. ) & | 4 0 | 0 0 4 0 0 | * * 288 * * * | 1 0 0 1 1 0 0 0 | 1 1 0 1 verfA( xo3oo .. ..&#x ) & | 2 1 | 0 0 1 2 0 | * * * 1152 * * | 0 1 0 0 1 0 1 0 | 0 1 1 1 verfB( xo3oo .. ..&#x ) & | 0 3 | 0 0 0 0 3 | * * * * 384 * | 0 1 0 0 0 1 0 1 | 0 1 1 1 verf( xo .. .. ox&#x ) | 1 2 | 0 0 0 2 1 | * * * * * 1152 | 0 0 1 0 0 0 1 1 | 0 0 2 1 --------------------------+---------+----------------------+---------------------------+------------------------------+------------ trunc( x.3o.4o. .. ) & ♦ 24 0 | 12 0 24 0 0 | 8 0 6 0 0 0 | 48 * * * * * * * | 1 1 0 0 trunc( xo3oo .. ..&#x ) & ♦ 6 6 | 3 3 3 6 3 | 1 3 0 3 1 0 | * 384 * * * * * * | 0 1 1 0 trunc( xo .. .. ox&#x ) ♦ 4 8 | 2 4 0 8 4 | 0 4 0 0 0 4 | * * 288 * * * * * | 0 0 2 0 verf( x.3o.4o.3o. ) & ♦ 8 0 | 0 0 12 0 0 | 0 0 6 0 0 0 | * * * 48 * * * * | 1 0 0 1 verfA( xo3oo4oo ..&#x ) & ♦ 4 1 | 0 0 4 4 0 | 0 0 1 4 0 0 | * * * * 288 * * * | 0 1 0 1 verfB( xo3oo4oo ..&#x ) & ♦ 0 6 | 0 0 0 0 12 | 0 0 0 0 8 0 | * * * * * 48 * * | 0 1 0 1 verfA( xo3oo .. ox&#x ) & ♦ 2 2 | 0 0 1 4 1 | 0 0 0 2 0 2 | * * * * * * 576 * | 0 0 1 1 verfB( xo3oo .. ox&#x ) & ♦ 1 3 | 0 0 0 3 3 | 0 0 0 0 1 3 | * * * * * * * 384 | 0 0 1 1 --------------------------+---------+----------------------+---------------------------+------------------------------+------------ trunc( x.3o.4o.3o. ) & ♦ 192 0 | 96 0 288 0 0 | 96 0 144 0 0 0 | 24 0 0 24 0 0 0 0 | 2 * * * trunc( xo3oo4oo ..&#x ) & ♦ 24 12 | 12 6 24 24 12 | 8 12 6 24 8 0 | 1 8 0 0 6 1 0 0 | * 48 * * trunc( xo3oo .. ox&#x ) & ♦ 8 12 | 4 6 3 18 9 | 1 9 0 6 2 12 | 0 2 3 0 0 0 3 2 | * * 192 * verf( xo3oo4oo3ox&#x ) ♦ 8 6 | 0 0 12 24 12 | 0 0 6 24 8 24 | 0 0 0 1 6 1 12 8 | * * * 48
xuxo3xooo4ooox3oxux&#xt → all heights = sqrt[sqrt(2)-1] = 0.643594 (tico || (u,x)-spic || (x,u)-spic || inv. tico) o...3o...4o...3o... | 192 * * * | 1 3 3 0 0 0 0 0 0 | 3 3 3 6 3 0 0 0 0 0 0 0 | 3 1 6 3 3 3 1 0 0 0 0 0 0 0 0 | 1 3 3 3 1 0 0 0 .o..3.o..4.o..3.o.. | * 144 * * | 0 0 4 4 1 0 0 0 0 | 0 0 4 4 8 4 4 0 0 0 0 0 | 0 0 4 8 1 4 4 1 0 0 0 0 0 0 0 | 0 1 4 4 1 1 0 0 ..o.3..o.4..o.3..o. | * * 144 * | 0 0 0 0 1 4 4 0 0 | 0 0 4 0 0 0 4 4 8 4 0 0 | 0 0 4 8 0 0 0 0 4 1 4 4 1 0 0 | 0 1 4 4 0 1 1 0 ...o3...o4...o3...o | * * * 192 | 0 0 0 0 0 0 3 3 1 | 0 0 0 0 0 0 3 0 3 6 3 3 | 0 0 0 3 0 0 0 0 6 0 1 3 3 1 3 | 0 0 3 3 0 3 1 1 ------------------------+-----------------+-----------------------------------+-----------------------------------------------+-------------------------------------------------------+---------------------- x... .... .... .... | 2 0 0 0 | 96 * * * * * * * * | 3 0 3 0 0 0 0 0 0 0 0 0 | 3 0 6 3 0 0 0 0 0 0 0 0 0 0 0 | 1 3 3 1 0 0 0 0 .... x... .... .... | 2 0 0 0 | * 288 * * * * * * * | 1 2 0 2 0 0 0 0 0 0 0 0 | 2 1 2 0 2 1 0 0 0 0 0 0 0 0 0 | 1 2 1 0 1 0 0 0 oo..3oo..4oo..3oo..&#x | 1 1 0 0 | * * 576 * * * * * * | 0 0 1 2 2 0 0 0 0 0 0 0 | 0 0 2 2 1 2 1 0 0 0 0 0 0 0 0 | 0 1 2 1 1 0 0 0 .... .... .... ..x. | 0 2 0 0 | * * * 288 * * * * * | 0 0 0 0 2 2 1 0 0 0 0 0 | 0 0 0 2 0 1 2 1 2 0 0 0 0 0 0 | 0 0 1 2 1 1 0 0 .oo.3.oo.4.oo.3.oo.&#x | 0 1 1 0 | * * * * 144 * * * * ♦ 0 0 4 0 0 0 4 0 0 0 0 0 | 0 0 4 8 0 0 0 0 4 0 0 0 0 0 0 | 0 1 4 4 0 1 0 0 ..x. .... .... .... | 0 0 2 0 | * * * * * 288 * * * | 0 0 1 0 0 0 0 2 2 0 0 0 | 0 0 2 2 0 0 0 0 0 1 2 1 0 0 0 | 0 1 2 1 0 0 1 0 ..oo3..oo4..oo3..oo&#x | 0 0 1 1 | * * * * * * 576 * * | 0 0 0 0 0 0 1 0 2 2 0 0 | 0 0 0 2 0 0 0 0 2 0 1 2 1 0 0 | 0 0 1 2 0 1 1 0 .... .... ...x .... | 0 0 0 2 | * * * * * * * 288 * | 0 0 0 0 0 0 0 0 0 2 2 1 | 0 0 0 0 0 0 0 0 2 0 0 1 2 1 2 | 0 0 0 1 0 2 1 1 .... .... .... ...x | 0 0 0 2 | * * * * * * * * 96 | 0 0 0 0 0 0 3 0 0 0 0 3 | 0 0 0 3 0 0 0 0 6 0 0 0 0 0 3 | 0 0 1 3 0 3 0 1 ------------------------+-----------------+-----------------------------------+-----------------------------------------------+-------------------------------------------------------+---------------------- x...3x... .... .... | 6 0 0 0 | 3 3 0 0 0 0 0 0 0 | 96 * * * * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 .... x...4o... .... | 4 0 0 0 | 0 4 0 0 0 0 0 0 0 | * 144 * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 | 1 1 0 0 1 0 0 0 xux. .... .... ....&#xt | 2 2 2 0 | 1 0 2 0 2 1 0 0 0 | * * 288 * * * * * * * * * | 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | 0 1 2 1 0 0 0 0 .... xo.. .... ....&#x | 2 1 0 0 | 0 1 2 0 0 0 0 0 0 | * * * 576 * * * * * * * * | 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 0 1 0 0 0 .... .... .... ox..&#x | 1 2 0 0 | 0 0 2 1 0 0 0 0 0 | * * * * 576 * * * * * * * | 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 | 0 0 1 1 1 0 0 0 .... .... .o..3.x.. | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 | * * * * * 192 * * * * * * | 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 | 0 0 0 1 1 1 0 0 .... .... .... .xux&#xt | 0 2 2 2 | 0 0 0 1 2 0 2 0 1 | * * * * * * 288 * * * * * | 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 | 0 0 1 2 0 1 0 0 ..x.3..o. .... .... | 0 0 3 0 | 0 0 0 0 0 3 0 0 0 | * * * * * * * 192 * * * * | 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 | 0 1 1 0 0 0 1 0 ..xo .... .... ....&#x | 0 0 2 1 | 0 0 0 0 0 1 2 0 0 | * * * * * * * * 576 * * * | 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 | 0 0 1 1 0 0 1 0 .... .... ..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 0 2 1 0 | * * * * * * * * * 576 * * | 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 | 0 0 0 1 0 1 1 0 .... ...o4...x .... | 0 0 0 4 | 0 0 0 0 0 0 0 4 0 | * * * * * * * * * * 144 * | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 0 0 1 1 1 .... .... ...x3...x | 0 0 0 6 | 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * 96 | 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 | 0 0 0 1 0 2 0 1 ------------------------+-----------------+-----------------------------------+-----------------------------------------------+-------------------------------------------------------+---------------------- x...3x...4o... .... ♦ 24 0 0 0 | 12 24 0 0 0 0 0 0 0 | 8 6 0 0 0 0 0 0 0 0 0 0 | 24 * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 .... x...4o...3o... ♦ 8 0 0 0 | 0 12 0 0 0 0 0 0 0 | 0 6 0 0 0 0 0 0 0 0 0 0 | * 24 * * * * * * * * * * * * * | 1 0 0 0 1 0 0 0 xux.3xoo. .... ....&#xt ♦ 6 3 3 0 | 3 3 6 0 3 3 0 0 0 | 1 0 3 3 0 0 0 1 0 0 0 0 | * * 192 * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 xuxo .... .... oxux&#xt ♦ 2 4 4 2 | 1 0 4 2 4 2 4 0 1 | 0 0 2 0 2 0 2 0 2 0 0 0 | * * * 288 * * * * * * * * * * * | 0 0 1 1 0 0 0 0 .... xo..4oo.. ....&#x ♦ 4 1 0 0 | 0 4 4 0 0 0 0 0 0 | 0 1 0 4 0 0 0 0 0 0 0 0 | * * * * 144 * * * * * * * * * * | 0 1 0 0 1 0 0 0 .... xo.. .... ox..&#x ♦ 2 2 0 0 | 0 1 4 1 0 0 0 0 0 | 0 0 0 2 2 0 0 0 0 0 0 0 | * * * * * 288 * * * * * * * * * | 0 0 1 0 1 0 0 0 .... .... oo..3ox..&#x ♦ 1 3 0 0 | 0 0 3 3 0 0 0 0 0 | 0 0 0 0 3 1 0 0 0 0 0 0 | * * * * * * 192 * * * * * * * * | 0 0 0 1 1 0 0 0 .... .o..4.o..3.x.. ♦ 0 6 0 0 | 0 0 0 12 0 0 0 0 0 | 0 0 0 0 0 8 0 0 0 0 0 0 | * * * * * * * 24 * * * * * * * | 0 0 0 0 1 1 0 0 .... .... .oox3.xux&#xt ♦ 0 3 3 6 | 0 0 0 3 3 0 6 3 3 | 0 0 0 0 0 1 3 0 0 3 0 1 | * * * * * * * * 192 * * * * * * | 0 0 0 1 0 1 0 0 ..x.3..o.4..o. .... ♦ 0 0 6 0 | 0 0 0 0 0 12 0 0 0 | 0 0 0 0 0 0 0 8 0 0 0 0 | * * * * * * * * * 24 * * * * * | 0 1 0 0 0 0 1 0 ..xo3..oo .... ....&#x ♦ 0 0 3 1 | 0 0 0 0 0 3 3 0 0 | 0 0 0 0 0 0 0 1 3 0 0 0 | * * * * * * * * * * 192 * * * * | 0 0 1 0 0 0 1 0 ..xo .... ..ox ....&#x ♦ 0 0 2 2 | 0 0 0 0 0 1 4 1 0 | 0 0 0 0 0 0 0 0 2 2 0 0 | * * * * * * * * * * * 288 * * * | 0 0 0 1 0 0 1 0 .... ..oo4..ox ....&#x ♦ 0 0 1 4 | 0 0 0 0 0 0 4 4 0 | 0 0 0 0 0 0 0 0 0 4 1 0 | * * * * * * * * * * * * 144 * * | 0 0 0 0 0 1 1 0 ...o3...o4...x .... ♦ 0 0 0 8 | 0 0 0 0 0 0 0 12 0 | 0 0 0 0 0 0 0 0 0 0 6 0 | * * * * * * * * * * * * * 24 * | 0 0 0 0 0 0 1 1 .... ...o4...x3...x ♦ 0 0 0 24 | 0 0 0 0 0 0 0 24 12 | 0 0 0 0 0 0 0 0 0 0 6 8 | * * * * * * * * * * * * * * 24 | 0 0 0 0 0 1 0 1 ------------------------+-----------------+-----------------------------------+-----------------------------------------------+-------------------------------------------------------+---------------------- x...3x...4o...3o... ♦ 192 0 0 0 | 96 288 0 0 0 0 0 0 0 | 96 144 0 0 0 0 0 0 0 0 0 0 | 24 24 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * xux.3xoo.4ooo. ....&#xt ♦ 24 6 6 0 | 12 24 24 0 6 12 0 0 0 | 8 6 12 24 0 0 0 8 0 0 0 0 | 1 0 8 0 6 0 0 0 0 1 0 0 0 0 0 | * 24 * * * * * * xuxo3xooo .... oxux&#xt ♦ 6 6 6 6 | 3 3 12 3 6 6 6 0 1 | 1 0 6 6 6 0 3 2 6 0 0 0 | 0 0 2 3 0 3 0 0 0 0 2 0 0 0 0 | * * 96 * * * * * xuxo .... ooox3oxux&#xt ♦ 6 6 6 6 | 1 0 6 6 6 3 12 3 3 | 0 0 3 0 6 2 6 0 6 6 0 1 | 0 0 0 3 0 0 2 0 2 0 0 3 0 0 0 | * * * 96 * * * * .... xo..4oo..3ox..&#x ♦ 8 6 0 0 | 0 12 24 12 0 0 0 0 0 | 0 6 0 24 24 8 0 0 0 0 0 0 | 0 1 0 0 6 12 8 1 0 0 0 0 0 0 0 | * * * * 24 * * * .... .ooo4.oox3.xux&#xt ♦ 0 6 6 24 | 0 0 0 12 6 0 24 24 12 | 0 0 0 0 0 8 12 0 0 24 6 8 | 0 0 0 0 0 0 0 1 8 0 0 0 6 0 1 | * * * * * 24 * * ..xo3..oo4..ox ....&#x ♦ 0 0 6 8 | 0 0 0 0 0 12 24 12 0 | 0 0 0 0 0 0 0 8 24 24 6 0 | 0 0 0 0 0 0 0 0 0 1 8 12 6 1 0 | * * * * * * 24 * ...o3...o4...x3...x ♦ 0 0 0 192 | 0 0 0 0 0 0 0 288 96 | 0 0 0 0 0 0 0 0 0 0 144 96 | 0 0 0 0 0 0 0 0 0 0 0 0 0 24 24 | * * * * * * * 1
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