| Acronym | (N,M)-dafupap |
| Name |
(N,M)-duoantifastegiaprismatic alterprism, (N,M)-duoantifastegiaprism atop lacing-ortho (N,M)-duoantifastegiaprism |
| Circumradius | ... |
|
Lace city in approx. ASCII-art |
xNo xMo xNo oMx
(1) (3)
oNx xMo oNx oMx
(2) (4)
|
| Face vector | 4nm, 24nm, 52nm+4n+4m, 52nm+14n+14m, 24nm+18n+18m+4, 4nm+10n+10m+6, 2n+2m+4 |
| Especially | tridafupap (N=M=3) |
| Confer |
|
For non-convex cases use N = n/d and M = m/b.
Incidence matrix according to Dynkin symbol
xoNox xxMoo &#x || xoNox ooMxx &#x → height(1,2) = height(3,4) = sqrt[(1+2 cos(pi/N))/(2+2 cos(pi/N))] = height of N-ap height(1,3) = height(2,4) = sqrt[(1+2 cos(pi/M))/(2+2 cos(pi/M))] = height of M-ap height(1,4) = height(2,3) = sqrt([2-1/(1+cos(pi/N))-1/(1+cos(pi/M))]/2) = height of (N,M)-dafup ((N,M)-dafup || lacing-ortho (N,M)-dafup) o.No. o.Mo. .. .. .. .. & | 4nm | 2 2 2 2 4 | 1 4 1 3 4 4 3 6 6 12 | 2 2 1 6 2 2 6 1 2 5 4 2 10 8 10 8 4 | 1 2 3 3 2 3 3 6 8 7 7 5 6 6 6 | 1 1 1 5 4 5 4 2 9 2 | 3 3 3 ------------------------------------+-----+---------------------+----------------------------------------+-------------------------------------------------------------+---------------------------------------------------+-----------------------------+-------- x. .. .. .. .. .. .. .. & | 2 | 4nm * * * * | 1 2 0 1 0 2 0 2 0 0 | 2 1 1 2 0 2 3 0 2 2 1 0 4 2 0 0 0 | 1 2 1 3 1 3 1 6 3 3 2 1 0 2 0 | 1 1 1 5 4 2 1 2 3 0 | 3 3 1 .. .. x. .. .. .. .. .. & | 2 | * 4nm * * * | 0 2 1 0 2 0 1 0 2 0 | 1 2 0 3 2 0 2 1 0 2 1 2 0 0 4 2 0 | 1 1 3 1 2 1 3 0 3 2 3 1 6 0 2 | 1 1 1 2 1 5 4 0 3 2 | 3 1 3 ooNoo ooMoo &#x .. .. .. .. & | 2 | * * 4nm * * | 0 0 0 2 2 0 0 0 0 4 | 0 0 1 4 1 0 0 0 0 0 0 0 4 4 4 2 2 | 0 2 2 0 0 0 0 4 4 2 4 2 2 4 3 | 1 0 0 4 4 2 2 2 6 1 | 2 3 2 o.No. o.Mo. || o.No. o.Mo. & | 2 | * * * 4nm * | 0 0 0 0 0 2 2 0 0 4 | 0 0 0 0 0 1 4 1 0 0 0 0 4 2 4 4 2 | 0 0 0 2 2 0 0 2 4 4 2 2 4 3 4 | 0 1 0 2 2 4 2 1 6 2 | 2 2 3 o.No. o.Mo. || .oN.o .oM.o & | 2 | * * * * 8nm | 0 0 0 0 0 0 0 2 2 2 | 0 0 0 0 0 0 0 0 1 2 2 1 2 2 2 2 1 | 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 | 0 0 1 2 2 2 2 1 4 1 | 2 2 2 ------------------------------------+-----+---------------------+----------------------------------------+-------------------------------------------------------------+---------------------------------------------------+-----------------------------+-------- x.No. .. .. .. .. .. .. & | n | n 0 0 0 0 | 4m * * * * * * * * * | 2 0 1 0 0 2 0 0 2 0 0 0 0 0 0 0 0 | 1 2 0 3 0 3 0 6 0 0 0 0 0 0 0 | 1 1 1 5 4 0 0 2 0 0 | 3 3 0 x. .. x. .. .. .. .. .. & | 4 | 2 2 0 0 0 | * 4nm * * * * * * * * | 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 | 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 | 1 1 1 2 1 2 1 0 1 0 | 3 1 1 .. .. x.Mo. .. .. .. .. & | m | 0 m 0 0 0 | * * 4n * * * * * * * | 0 2 0 0 2 0 0 1 0 0 0 2 0 0 0 0 0 | 1 0 3 0 2 0 3 0 0 0 0 0 6 0 0 | 1 1 1 0 0 5 4 0 0 2 | 3 0 3 xo .. .. .. &#x .. .. .. .. & | 3 | 1 0 2 0 0 | * * * 4nm * * * * * * | 0 0 1 2 0 0 0 0 0 0 0 0 2 2 0 0 0 | 0 2 1 0 0 0 0 4 2 1 2 1 0 2 0 | 1 0 0 4 2 1 1 2 3 0 | 2 3 1 .. .. xx .. &#x .. .. .. .. & | 4 | 0 2 2 0 0 | * * * * 4nm * * * * * | 0 0 0 2 1 0 0 0 0 0 0 0 0 0 2 0 0 | 0 1 2 0 0 0 0 0 2 0 2 0 2 0 1 | 1 0 0 2 0 2 2 0 2 1 | 2 1 2 x. .. .. .. || x. .. .. .. & | 4 | 2 0 0 2 0 | * * * * * 4nm * * * * | 0 0 0 0 0 1 2 0 0 0 0 0 2 0 0 0 0 | 0 0 0 2 1 0 0 2 2 2 0 0 0 1 0 | 0 1 0 2 2 2 0 1 2 0 | 2 2 1 .. .. x. .. || .. .. o. .. & | 3 | 0 1 0 2 0 | * * * * * * 4nm * * * | 0 0 0 0 0 0 2 1 0 0 0 0 0 0 2 2 0 | 0 0 0 1 2 0 0 0 2 2 1 1 4 0 2 | 0 1 0 1 1 4 2 0 3 2 | 2 1 3 x. .. .. .. || .o .. .. .. & | 3 | 1 0 0 0 2 | * * * * * * * 8nm * * | 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 | 0 0 0 0 0 2 1 2 1 1 1 1 0 1 0 | 0 0 1 2 2 1 1 1 2 0 | 2 2 1 .. .. x. .. || .. .. .o .. & | 3 | 0 1 0 0 2 | * * * * * * * * 8nm * | 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 | 0 0 0 0 0 1 2 0 1 1 1 1 2 0 1 | 0 0 1 1 1 2 2 0 2 1 | 2 1 2 ooNoo ooMoo &#x || o.No. o.Mo. & | 3 | 0 0 1 1 1 | * * * * * * * * * 16nm | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 | 0 0 0 0 0 0 0 1 1 1 1 1 1 2 2 | 0 0 0 1 1 1 1 1 4 1 | 1 2 2 ------------------------------------+-----+---------------------+----------------------------------------+-------------------------------------------------------------+---------------------------------------------------+-----------------------------+-------- x.No. x. .. .. .. .. .. & ♦ 2n | 2n n 0 0 0 | 2 n 0 0 0 0 0 0 0 0 | 4m * * * * * * * * * * * * * * * * | 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 | 1 1 1 2 1 0 0 0 0 0 | 3 1 0 x. .. x.Mo. .. .. .. .. & ♦ 2m | m 2m 0 0 0 | 0 m 2 0 0 0 0 0 0 0 | * 4n * * * * * * * * * * * * * * * | 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 2 1 0 0 0 | 3 0 1 xoNox .. .. &#x .. .. .. .. & ♦ 2n | 2n 0 2n 0 0 | 2 0 0 2n 0 0 0 0 0 0 | * * 2m * * * * * * * * * * * * * * | 0 2 0 0 0 0 0 4 0 0 0 0 0 0 0 | 1 0 0 4 2 0 0 2 0 0 | 2 3 0 xo .. xx .. &#x .. .. .. .. & ♦ 6 | 2 3 4 0 0 | 0 1 0 2 2 0 0 0 0 0 | * * * 4nm * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 | 1 0 0 2 0 1 1 0 1 0 | 2 1 1 .. .. xxMoo &#x .. .. .. .. & ♦ 2m | 0 2m m 0 0 | 0 0 2 0 m 0 0 0 0 0 | * * * * 4n * * * * * * * * * * * * | 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 | 1 0 0 0 0 2 2 0 0 1 | 2 0 2 x.No. .. .. || x.No. .. .. & ♦ 2n | 2n 0 0 n 0 | 2 0 0 0 0 n 0 0 0 0 | * * * * * 4m * * * * * * * * * * * | 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 | 0 1 0 2 2 0 0 1 0 0 | 2 2 0 x. .. x. .. || x. .. o. .. & ♦ 6 | 3 2 0 4 0 | 0 1 0 0 0 2 2 0 0 0 | * * * * * * 4nm * * * * * * * * * * | 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 | 0 1 0 1 1 2 0 0 1 0 | 2 1 1 .. .. x.Mo. || .. .. o.Mx. & ♦ 2m | 0 2m 0 2m 0 | 0 0 2 0 0 0 2m 0 0 0 | * * * * * * * 2n * * * * * * * * * | 0 0 0 0 2 0 0 0 0 0 0 0 4 0 0 | 0 1 0 0 0 4 2 0 0 2 | 2 0 3 x.No. .. .. || .oN.x .. .. & ♦ 2n | 2n 0 0 0 2n | 2 0 0 0 0 0 0 2n 0 0 | * * * * * * * * 4m * * * * * * * * | 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 | 0 0 1 2 2 0 0 1 0 0 | 2 2 0 x. .. x. .. || .o .. .o .. & ♦ 5 | 2 2 0 0 4 | 0 1 0 0 0 0 0 2 2 0 | * * * * * * * * * 4nm * * * * * * * | 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 | 0 0 1 1 1 1 1 0 1 0 | 2 1 1 x. .. .. o. || .o .. .. .x & ♦ 4 | 1 1 0 0 4 | 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * 4nm * * * * * * | 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 | 0 0 1 1 1 1 1 0 1 0 | 2 1 1 .. .. x.Mo. || .. .. .oM.x & ♦ 2m | 0 2m 0 0 2m | 0 0 2 0 0 0 0 0 2m 0 | * * * * * * * * * * * 4n * * * * * | 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 | 0 0 1 0 0 2 2 0 0 1 | 2 0 2 xo .. .. .. &#x || x. .. .. .. & ♦ 5 | 2 0 2 2 2 | 0 0 0 1 0 1 0 1 0 2 | * * * * * * * * * * * * 8nm * * * * | 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 | 0 0 0 1 1 1 0 1 2 0 | 1 2 1 .. ox .. .. &#x || .. o. .. .. & ♦ 4 | 1 0 2 1 2 | 0 0 0 1 0 0 0 1 0 2 | * * * * * * * * * * * * * 8nm * * * | 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 | 0 0 0 1 1 0 1 1 2 0 | 1 2 1 .. .. xx .. &#x || .. .. o. .. & ♦ 5 | 0 2 2 2 2 | 0 0 0 0 1 0 1 0 1 2 | * * * * * * * * * * * * * * 8nm * * | 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 | 0 0 0 1 0 1 1 0 2 1 | 1 1 2 .. .. .. oo &#x || .. .. .. x. & ♦ 4 | 0 1 1 2 2 | 0 0 0 0 0 0 1 0 1 2 | * * * * * * * * * * * * * * * 8nm * | 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 | 0 0 0 0 1 1 1 0 2 1 | 1 1 2 ooNoo ooMoo &#x || ooNoo ooMoo &#x ♦ 4 | 0 0 2 2 2 | 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * * * * 4nm | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 0 0 1 4 1 | 0 2 2 ------------------------------------+-----+---------------------+----------------------------------------+-------------------------------------------------------------+---------------------------------------------------+-----------------------------+-------- x.No. x.Mo. .. .. .. .. & ♦ nm | nm nm 0 0 0 | m nm n 0 0 0 0 0 0 0 | m n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 3 0 0 xoNox xx .. &#x .. .. .. .. & ♦ 4n | 4n 2n 4n 0 0 | 4 2n 0 4n 2n 0 0 0 0 0 | 2 0 2 2n 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 2m * * * * * * * * * * * * * | 1 0 0 2 0 0 0 0 0 0 | 2 1 0 xo .. xxMoo &#x .. .. .. .. & ♦ 3m | m 3m 2m 0 0 | 0 m 3 m 2m 0 0 0 0 0 | 0 1 0 m 2 0 0 0 0 0 0 0 0 0 0 0 0 | * * 4n * * * * * * * * * * * * | 1 0 0 0 0 1 1 0 0 0 | 2 0 1 x.No. x. .. || x.No. o. .. & ♦ 3n | 3n n 0 2n 0 | 3 n 0 0 0 2n n 0 0 0 | 1 0 0 0 0 2 n 0 0 0 0 0 0 0 0 0 0 | * * * 4m * * * * * * * * * * * | 0 1 0 1 1 0 0 0 0 0 | 2 1 0 x. .. x.Mo. || x. .. o.Mx. & ♦ 4m | 2m 4m 0 4m 0 | 0 2m 4 0 0 2m 4m 0 0 0 | 0 2 0 0 0 0 2m 2 0 0 0 0 0 0 0 0 0 | * * * * 2n * * * * * * * * * * | 0 1 0 0 0 2 0 0 0 0 | 2 0 1 x.No. x. .. || .oN.x .o .. & ♦ 3n | 3n n 0 0 4n | 3 n 0 0 0 0 0 4n 2n 0 | 1 0 0 0 0 0 0 0 2 n n 0 0 0 0 0 0 | * * * * * 4m * * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 | 2 1 0 x. .. x.Mo. || .o .. .oM.x & ♦ 3m | m 3m 0 0 4m | 0 m 3 0 0 0 0 2m 4m 0 | 0 1 0 0 0 0 0 0 0 m m 2 0 0 0 0 0 | * * * * * * 4n * * * * * * * * | 0 0 1 0 0 1 1 0 0 0 | 2 0 1 xoNox .. .. &#x || x.No. .. .. & ♦ 3n | 3n 0 2n n 2n | 3 0 0 2n 0 n 0 2n 0 2n | 0 0 1 0 0 1 0 0 1 0 0 0 n n 0 0 0 | * * * * * * * 8m * * * * * * * | 0 0 0 1 1 0 0 1 0 0 | 1 2 0 xo .. xx .. &#x || x. .. o. .. & ♦ 8 | 3 3 4 4 4 | 0 1 0 2 2 2 2 2 2 4 | 0 0 0 1 0 0 1 0 0 0 1 0 2 0 2 0 0 | * * * * * * * * 4nm * * * * * * | 0 0 0 1 0 1 0 0 1 0 | 1 1 1 xo .. .. oo &#x || x. .. .. x. & ♦ 7 | 3 2 2 4 4 | 0 1 0 1 0 2 2 2 2 4 | 0 0 0 0 0 0 1 0 0 1 0 0 2 0 0 2 0 | * * * * * * * * * 4nm * * * * * | 0 0 0 0 1 1 0 0 1 0 | 1 1 1 .. ox xx .. &#x || .. o. o. .. & ♦ 7 | 2 3 4 2 4 | 0 1 0 2 2 0 1 2 2 4 | 0 0 0 1 0 0 0 0 0 1 0 0 0 2 2 0 0 | * * * * * * * * * * 4nm * * * * | 0 0 0 1 0 0 1 0 1 0 | 1 1 1 .. ox .. oo &#x || .. o. .. x. & ♦ 5 | 1 1 2 2 4 | 0 0 0 1 0 0 1 2 2 4 | 0 0 0 0 0 0 0 0 0 0 1 0 0 2 0 2 0 | * * * * * * * * * * * 4nm * * * | 0 0 0 0 1 0 1 0 1 0 | 1 1 1 .. .. xxMoo &#x || .. .. o.Mx. & ♦ 3m | 0 3m m 2m 2m | 0 0 3 0 m 0 2m 0 2m 2m | 0 0 0 0 1 0 0 1 0 0 0 1 0 0 m m 0 | * * * * * * * * * * * * 8n * * | 0 0 0 0 0 1 1 0 0 1 | 1 0 2 xo .. .. .. &#x || xo .. .. .. &#x & ♦ 6 | 2 0 4 3 4 | 0 0 0 2 0 1 0 2 0 8 | 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 2 | * * * * * * * * * * * * * 4nm * | 0 0 0 0 0 0 0 1 2 0 | 0 2 1 .. .. xx .. &#x || .. .. oo .. &#x & ♦ 6 | 0 2 3 4 4 | 0 0 0 0 1 0 2 0 2 8 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 | * * * * * * * * * * * * * * 4nm | 0 0 0 0 0 0 0 0 2 1 | 0 1 2 ------------------------------------+-----+---------------------+----------------------------------------+-------------------------------------------------------------+---------------------------------------------------+-----------------------------+-------- xoNox xxMoo &#x .. .. .. .. & ♦ 2nm | 2nm 2nm 2nm 0 0 | 2m 2nm 2n 2nm 2nm 0 0 0 0 0 | 2m 2n m 2nm 2n 0 0 0 0 0 0 0 0 0 0 0 0 | 2 m 2n 0 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * | 2 0 0 x.No. x.Mo. || x.No. o.Mx. & ♦ 2nm | 2nm 2nm 0 2nm 0 | 2m 2nm 2n 0 0 2nm 2nm 0 0 0 | 2m 2n 0 0 0 2m 2nm n 0 0 0 0 0 0 0 0 0 | 2 0 0 2m n 0 0 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * | 2 0 0 x.No. x.Mo. || .oN.x .oM.x & ♦ 2nm | 2nm 2nm 0 0 4nm | 2m 2nm 2n 0 0 0 0 4nm 4nm 0 | 2m 2n 0 0 0 0 0 0 2m 2nm 2nm 2n 0 0 0 0 0 | 2 0 0 0 0 2m 2n 0 0 0 0 0 0 0 0 | * * 2 * * * * * * * | 2 0 0 xoNox xx .. &#x || x.No. o. .. & ♦ 5n | 5n 2n 4n 2n 4n | 5 2n 0 4n 2n 2n n 4n 2n 4n | 2 0 2 2n 0 2 n 0 2 n n 0 2n 2n 2n 0 0 | 0 1 0 1 0 1 0 2 n 0 n 0 0 0 0 | * * * 4m * * * * * * | 1 1 0 xoNox .. oo &#x || x.No. .. x. & ♦ 4n | 4n n 2n 2n 4n | 4 n 0 2n 0 2n n 4n 2n 4n | 1 0 1 0 0 2 n 0 2 n n 0 2n 2n 0 2n 0 | 0 0 0 1 0 1 0 2 0 n 0 n 0 0 0 | * * * * 4m * * * * * | 1 1 0 xo .. xxMoo &#x || x. .. o.Mx. & ♦ 5m | 2m 5m 2m 4m 4m | 0 2m 5 m 2m 2m 4m 2m 4m 4m | 0 2 0 m 2 0 2m 2 0 m m 2 2m 0 2m 2m 0 | 0 0 1 0 1 0 1 0 m m 0 0 2 0 0 | * * * * * 4n * * * * | 1 0 1 .. ox xxMoo &#x || .. o. o.Mx. & ♦ 4m | m 4m 2m 2m 4m | 0 m 4 m 2m 0 2m 2m 4m 4m | 0 1 0 m 2 0 0 1 0 m m 2 0 2m 2m 2m 0 | 0 0 1 0 0 0 1 0 0 0 m m 2 0 0 | * * * * * * 4n * * * | 1 0 1 xoNox .. .. &#x || xoNox .. .. &#x ♦ 4n | 4n 0 4n 2n 4n | 4 0 0 4n 0 2n 0 4n 0 8n | 0 0 2 0 0 2 0 0 2 0 0 0 4n 4n 0 0 2n | 0 0 0 0 0 0 0 4 0 0 0 0 0 2n 0 | * * * * * * * 2m * * | 0 2 0 xo .. xx .. &#x || xo .. oo .. &#x & ♦ 9 | 3 3 6 6 8 | 0 1 0 3 2 2 3 4 4 16 | 0 0 0 1 0 0 1 0 0 1 1 0 4 4 4 4 4 | 0 0 0 0 0 0 0 0 1 1 1 1 0 2 2 | * * * * * * * * 4nm * | 0 1 1 .. .. xxMoo &#x || .. .. ooMxx &#x ♦ 4m | 0 4m 2m 4m 4m | 0 0 4 0 2m 0 4m 0 4m 8m | 0 0 0 0 2 0 0 2 0 0 0 2 0 0 4m 4m 2m | 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2m | * * * * * * * * * 2n | 0 0 2 ------------------------------------+-----+---------------------+----------------------------------------+-------------------------------------------------------------+---------------------------------------------------+-----------------------------+-------- xoNox xxMoo &#x || x.No. o.Mx. & ♦ 3nm | 3nm 3nm 2nm 2nm 4nm | 3m 3nm 3n 2nm 2nm 2nm 2nm 4nm 4nm 4nm | 3m 3n m 2nm 2n 2m 2nm n 2m 2nm 2nm 2n 2nm 2nm 2nm 2nm 0 | 3 m 2n 2m n 2m 2n 2m nm nm nm nm 2n 0 0 | 1 1 1 m m n n 0 0 0 | 4 * * xoNox xx .. &#x || xoNox oo .. &#x & ♦ 6n | 6n 2n 6n 4n 8n | 6 2n 0 6n 2n 4n 2n 8n 4n 16n | 2 0 3 2n 0 4 2n 0 4 2n 2n 0 8n 8n 4n 4n 4n | 0 1 0 2 0 2 0 8 2n 2n 2n 2n 0 4n 2n | 0 0 0 2 2 0 0 2 2n 0 | * 2m * xo .. xxMoo &#x || xo .. ooMxx &#x & ♦ 6m | 2m 6m 4m 6m 8m | 0 2m 6 2m 4m 2m 6m 4m 8m 16m | 0 2 0 2m 4 0 2m 3 0 2m 2m 4 4m 4m 8m 8m 4m | 0 0 2 0 1 0 2 0 2m 2m 2m 2m 8 2m 4m | 0 0 0 0 0 2 2 0 2m 2 | * * 2n
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