Acronym | rasa (old: ras) | ||
Name |
rectified hepteract, equatorial cross-section of roc-first bro | ||
Circumradius | sqrt(3) = 1.732051 | ||
Inradius wrt. hop | 6/sqrt(14) = 1.603567 | ||
Inradius wrt. rax | 1/sqrt(2) = 0.707107 | ||
Lace city in approx. ASCII-art |
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Coordinates | (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0) & all permutations, all changes of sign | ||
Volume | 5039 sqrt(2)/630 = 11.311464 | ||
Surface | (5033+sqrt(7)/45 = 111.903239 | ||
Dihedral angles | |||
Face vector | 448, 2688, 5152, 5040, 2968, 980, 142 | ||
Confer |
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External links |
Incidence matrix according to Dynkin symbol
o3o3o3o3o3x4o . . . . . . . | 448 | 12 | 30 6 | 40 15 | 30 20 | 12 15 | 2 6 --------------+-----+------+----------+----------+----------+--------+------- . . . . . x . | 2 | 2688 | 5 1 | 10 5 | 10 10 | 5 10 | 1 5 --------------+-----+------+----------+----------+----------+--------+------- . . . . o3x . | 3 | 3 | 4480 * | 4 1 | 6 4 | 4 6 | 1 4 . . . . . x4o | 4 | 4 | * 672 ♦ 0 5 | 0 10 | 0 10 | 0 5 --------------+-----+------+----------+----------+----------+--------+------- . . . o3o3x . ♦ 4 | 6 | 4 0 | 4480 * | 3 1 | 3 3 | 1 3 . . . . o3x4o ♦ 12 | 24 | 8 6 | * 560 ♦ 0 4 | 0 6 | 0 4 --------------+-----+------+----------+----------+----------+--------+------- . . o3o3o3x . ♦ 5 | 10 | 10 0 | 5 0 | 2688 * | 2 1 | 1 2 . . . o3o3x4o ♦ 32 | 96 | 64 24 | 16 8 | * 280 | 0 3 | 0 3 --------------+-----+------+----------+----------+----------+--------+------- . o3o3o3o3x . ♦ 6 | 15 | 20 0 | 15 0 | 6 0 | 896 * | 1 1 . . o3o3o3x4o ♦ 80 | 320 | 320 80 | 160 40 | 32 10 | * 84 | 0 2 --------------+-----+------+----------+----------+----------+--------+------- o3o3o3o3o3x . ♦ 7 | 21 | 35 0 | 35 0 | 21 0 | 7 0 | 128 * . o3o3o3o3x4o ♦ 192 | 960 | 1280 240 | 960 160 | 384 60 | 64 12 | * 14
o3o3o3o3o3x4/3o . . . . . . . | 448 | 12 | 30 6 | 40 15 | 30 20 | 12 15 | 2 6 ----------------+-----+------+----------+----------+----------+--------+------- . . . . . x . | 2 | 2688 | 5 1 | 10 5 | 10 10 | 5 10 | 1 5 ----------------+-----+------+----------+----------+----------+--------+------- . . . . o3x . | 3 | 3 | 4480 * | 4 1 | 6 4 | 4 6 | 1 4 . . . . . x4/3o | 4 | 4 | * 672 ♦ 0 5 | 0 10 | 0 10 | 0 5 ----------------+-----+------+----------+----------+----------+--------+------- . . . o3o3x . ♦ 4 | 6 | 4 0 | 4480 * | 3 1 | 3 3 | 1 3 . . . . o3x4/3o ♦ 12 | 24 | 8 6 | * 560 ♦ 0 4 | 0 6 | 0 4 ----------------+-----+------+----------+----------+----------+--------+------- . . o3o3o3x . ♦ 5 | 10 | 10 0 | 5 0 | 2688 * | 2 1 | 1 2 . . . o3o3x4/3o ♦ 32 | 96 | 64 24 | 16 8 | * 280 | 0 3 | 0 3 ----------------+-----+------+----------+----------+----------+--------+------- . o3o3o3o3x . ♦ 6 | 15 | 20 0 | 15 0 | 6 0 | 896 * | 1 1 . . o3o3o3x4/3o ♦ 80 | 320 | 320 80 | 160 40 | 32 10 | * 84 | 0 2 ----------------+-----+------+----------+----------+----------+--------+------- o3o3o3o3o3x . ♦ 7 | 21 | 35 0 | 35 0 | 21 0 | 7 0 | 128 * . o3o3o3o3x4/3o ♦ 192 | 960 | 1280 240 | 960 160 | 384 60 | 64 12 | * 14
x3o3x *b3o3o3o3o . . . . . . . | 448 | 6 6 | 15 6 15 | 15 20 20 | 20 15 15 | 15 6 6 | 6 1 1 -----------------+-----+-----------+---------------+---------------+---------------+------------+--------- x . . . . . . | 2 | 1344 * | 5 1 0 | 5 10 0 | 10 10 0 | 10 5 0 | 5 1 0 . . x . . . . | 2 | * 1344 | 0 1 5 | 5 0 10 | 10 0 10 | 10 0 5 | 5 0 1 -----------------+-----+-----------+---------------+---------------+---------------+------------+--------- x3o . . . . . | 3 | 3 0 | 2240 * * | 1 4 0 | 4 6 0 | 6 4 0 | 4 1 0 x . x . . . . | 4 | 2 2 | * 672 * ♦ 5 0 0 | 10 0 0 | 10 0 0 | 5 0 0 . o3x . . . . | 3 | 0 3 | * * 2240 | 1 0 4 | 4 0 6 | 6 0 4 | 4 0 1 -----------------+-----+-----------+---------------+---------------+---------------+------------+--------- x3o3x . . . . ♦ 12 | 12 12 | 4 6 4 | 560 * * ♦ 4 0 0 | 6 0 0 | 4 0 0 x3o . *b3o . . . ♦ 4 | 6 0 | 4 0 0 | * 2240 * | 1 3 0 | 3 3 0 | 3 1 0 . o3x *b3o . . . ♦ 4 | 0 6 | 0 0 4 | * * 2240 | 1 0 3 | 3 0 3 | 3 0 1 -----------------+-----+-----------+---------------+---------------+---------------+------------+--------- x3o3x *b3o . . . ♦ 32 | 48 48 | 32 24 32 | 8 8 8 | 280 * * | 3 0 0 | 3 0 0 x3o . *b3o3o . . ♦ 5 | 10 0 | 10 0 0 | 0 5 0 | * 1344 * | 1 2 0 | 2 1 0 . o3x *b3o3o . . ♦ 5 | 0 10 | 0 0 10 | 0 0 5 | * * 1344 | 1 0 2 | 2 0 1 -----------------+-----+-----------+---------------+---------------+---------------+------------+--------- x3o3x *b3o3o . . ♦ 80 | 160 160 | 160 80 160 | 40 80 80 | 10 16 16 | 84 * * | 2 0 0 x3o . *b3o3o3o . ♦ 6 | 15 0 | 20 0 0 | 0 15 0 | 0 6 0 | * 448 * | 1 1 0 . o3x *b3o3o3o . ♦ 6 | 0 15 | 0 0 20 | 0 0 15 | 0 0 6 | * * 448 | 1 0 1 -----------------+-----+-----------+---------------+---------------+---------------+------------+--------- x3o3x *b3o3o3o . ♦ 192 | 480 480 | 640 240 640 | 160 480 480 | 60 192 192 | 12 32 32 | 14 * * x3o . *b3o3o3o3o ♦ 7 | 21 0 | 35 0 0 | 0 35 0 | 0 21 0 | 0 7 0 | * 64 * . o3x *b3o3o3o3o ♦ 7 | 0 21 | 0 0 35 | 0 0 35 | 0 0 21 | 0 0 7 | * * 64
qo oo3oo3oo3oo3xo4oq&#zx → height = 0 (tegum sum of a q-height raxip and an equatorial q-ax) o. o.3o.3o.3o.3o.4o. | 384 * | 10 2 | 20 5 1 10 | 20 10 5 20 | 10 10 10 20 | 2 5 10 10 | 1 5 2 .o .o3.o3.o3.o3.o4.o | * 64 | 0 12 | 0 0 6 30 | 0 0 15 40 | 0 0 20 30 | 0 0 15 12 | 0 6 2 -------------------------+--------+----------+-------------------+-------------------+------------------+---------------+--------- .. .. .. .. .. x. .. | 2 0 | 1920 * | 4 1 0 1 | 6 4 1 4 | 4 6 4 6 | 1 4 6 4 | 1 4 1 oo oo3oo3oo3oo3oo4oo&#x | 1 1 | * 768 | 0 0 1 5 | 0 0 5 10 | 0 0 10 10 | 0 0 10 5 | 0 5 1 -------------------------+--------+----------+-------------------+-------------------+------------------+---------------+--------- .. .. .. .. o.3x. .. | 3 0 | 3 0 | 2560 * * * | 3 1 0 1 | 3 3 1 3 | 1 3 3 3 | 1 3 1 .. .. .. .. .. x.4o. | 4 0 | 4 0 | * 480 * * ♦ 0 4 1 0 | 0 6 4 0 | 0 4 6 0 | 1 4 0 qo .. .. .. .. .. oq&#zx | 2 2 | 0 4 | * * 192 * ♦ 0 0 5 0 | 0 0 10 0 | 0 0 10 0 | 0 5 0 .. .. .. .. .. xo ..&#x | 2 1 | 1 2 | * * * 1920 | 0 0 1 4 | 0 0 4 6 | 0 0 6 4 | 0 4 1 -------------------------+--------+----------+-------------------+-------------------+------------------+---------------+--------- .. .. .. o.3o.3x. .. ♦ 4 0 | 6 0 | 4 0 0 0 | 1920 * * * | 2 1 0 1 | 1 2 1 2 | 1 2 1 .. .. .. .. o.3x.4o. ♦ 12 0 | 24 0 | 8 6 0 0 | * 320 * * ♦ 0 3 1 0 | 0 3 3 0 | 1 3 0 qo .. .. .. .. xo4oq&#zx ♦ 8 4 | 8 16 | 0 2 4 8 | * * 240 * ♦ 0 0 4 0 | 0 0 6 0 | 0 4 0 .. .. .. .. oo3xo ..&#x ♦ 3 1 | 3 3 | 1 0 0 3 | * * * 2560 | 0 0 1 3 | 0 0 3 3 | 0 3 1 -------------------------+--------+----------+-------------------+-------------------+------------------+---------------+--------- .. .. o.3o.3o.3x. .. ♦ 5 0 | 10 0 | 10 0 0 0 | 5 0 0 0 | 768 * * * | 1 1 0 1 | 1 1 1 .. .. .. o.3o.3x.4o. ♦ 32 0 | 96 0 | 64 24 0 0 | 16 8 0 0 | * 120 * * | 0 2 1 0 | 1 2 0 qo .. .. .. oo3xo4oq&#zx ♦ 24 8 | 48 48 | 16 12 12 48 | 0 2 6 16 | * * 160 * | 0 0 3 0 | 0 3 0 .. .. .. oo3oo3xo ..&#x ♦ 4 1 | 6 4 | 4 0 0 6 | 1 0 0 4 | * * * 1920 | 0 0 1 2 | 0 2 1 -------------------------+--------+----------+-------------------+-------------------+------------------+---------------+--------- .. o.3o.3o.3o.3x. .. ♦ 6 0 | 15 0 | 20 0 0 0 | 15 0 0 0 | 6 0 0 0 | 128 * * * | 1 0 1 .. .. o.3o.3o.3x.4o. ♦ 80 0 | 320 0 | 320 80 0 0 | 160 40 0 0 | 32 10 0 0 | * 24 * * | 1 1 0 qo .. .. oo3oo3xo4oq&#zx ♦ 64 16 | 192 128 | 128 48 32 192 | 32 16 24 128 | 0 2 8 32 | * * 60 * | 0 2 0 .. .. oo3oo3oo3xo ..&#x ♦ 5 1 | 10 5 | 10 0 0 10 | 5 0 0 10 | 1 0 0 5 | * * * 768 | 0 1 1 -------------------------+--------+----------+-------------------+-------------------+------------------+---------------+--------- .. o.3o.3o.3o.3x.4o. ♦ 192 0 | 960 0 | 1280 240 0 0 | 960 160 0 0 | 384 60 0 0 | 64 12 0 0 | 2 * * qo .. oo3oo3oo3xo4oq&#zx ♦ 160 32 | 640 320 | 640 160 80 640 | 320 80 80 640 | 64 20 40 320 | 0 2 10 64 | * 12 * .. oo3oo3oo3oo3xo ..&#x ♦ 6 1 | 15 6 | 20 0 0 15 | 15 0 0 20 | 6 0 0 15 | 1 0 0 6 | * * 128
ooo3ooo3ooo3ooo3xox4oqo&#xt → both heights = = 1/sqrt(2) = 0.707107 (rax || pseudo q-ax || rax) o..3o..3o..3o..3o..4o.. | 192 * * | 10 2 0 0 | 20 5 10 1 0 0 0 | 20 10 20 5 0 0 0 | 10 10 20 10 0 0 0 | 2 5 10 10 0 0 0 | 1 2 5 0 0 .o.3.o.3.o.3.o.3.o.4.o. | * 64 * | 0 6 6 0 | 0 0 15 6 15 0 0 | 0 0 20 15 20 0 0 | 0 0 15 20 15 0 0 | 0 0 6 15 6 0 0 | 0 1 6 1 0 ..o3..o3..o3..o3..o4..o | * * 192 | 0 0 2 10 | 0 0 0 1 10 20 5 | 0 0 0 5 20 20 10 | 0 0 0 10 20 10 10 | 0 0 0 10 10 2 5 | 0 0 5 2 1 ----------------------------+------------+-----------------+-------------------------------+-------------------------------+---------------------------+------------------------+------------- ... ... ... ... x.. ... | 2 0 0 | 960 * * * | 4 1 1 0 0 0 0 | 6 4 4 1 0 0 0 | 4 6 6 4 0 0 0 | 1 4 4 6 0 0 0 | 1 1 4 0 0 oo.3oo.3oo.3oo.3oo.4oo.&#x | 1 1 0 | * 384 * * | 0 0 5 1 0 0 0 | 0 0 10 5 0 0 0 | 0 0 10 10 0 0 0 | 0 0 5 10 0 0 0 | 0 1 5 0 0 .oo3.oo3.oo3.oo3.oo4.oo&#x | 0 1 1 | * * 384 * | 0 0 0 1 5 0 0 | 0 0 0 5 10 0 0 | 0 0 0 10 10 0 0 | 0 0 0 10 5 0 0 | 0 0 5 1 0 ... ... ... ... ..x ... | 0 0 2 | * * * 960 | 0 0 0 0 1 4 1 | 0 0 0 1 4 6 4 | 0 0 0 4 6 4 6 | 0 0 0 6 4 1 4 | 0 0 4 1 1 ----------------------------+------------+-----------------+-------------------------------+-------------------------------+---------------------------+------------------------+------------- ... ... ... o..3x.. ... | 3 0 0 | 3 0 0 0 | 1280 * * * * * * | 3 1 1 0 0 0 0 | 3 3 3 1 0 0 0 | 1 3 3 3 0 0 0 | 1 1 3 0 0 ... ... ... ... x..4o.. | 4 0 0 | 4 0 0 0 | * 240 * * * * * ♦ 0 4 0 1 0 0 0 | 0 6 0 4 0 0 0 | 0 4 0 6 0 0 0 | 1 0 4 0 0 ... ... ... ... xo. ...&#x | 2 1 0 | 1 2 0 0 | * * 960 * * * * | 0 0 4 1 0 0 0 | 0 0 6 4 0 0 0 | 0 0 4 6 0 0 0 | 0 1 4 0 0 ... ... ... ... ... oqo&#xt | 1 2 1 | 0 2 2 0 | * * * 192 * * * ♦ 0 0 0 5 0 0 0 | 0 0 0 10 0 0 0 | 0 0 0 10 0 0 0 | 0 0 5 0 0 ... ... ... ... .ox ...&#x | 0 1 2 | 0 0 2 1 | * * * * 960 * * | 0 0 0 1 4 0 0 | 0 0 0 4 6 0 0 | 0 0 0 6 4 0 0 | 0 0 4 1 0 ... ... ... ..o3..x ... | 0 0 3 | 0 0 0 3 | * * * * * 1280 * | 0 0 0 0 1 3 1 | 0 0 0 1 3 3 3 | 0 0 0 3 3 1 3 | 0 0 3 1 1 ... ... ... ... ..x4..o | 0 0 4 | 0 0 0 4 | * * * * * * 240 ♦ 0 0 0 1 0 0 4 | 0 0 0 4 0 0 6 | 0 0 0 6 0 0 4 | 0 0 4 0 1 ----------------------------+------------+-----------------+-------------------------------+-------------------------------+---------------------------+------------------------+------------- ... ... o..3o..3x.. ... ♦ 4 0 0 | 6 0 0 0 | 4 0 0 0 0 0 0 | 960 * * * * * * | 2 1 1 0 0 0 0 | 1 2 2 1 0 0 0 | 1 1 2 0 0 ... ... ... o..3x..4o.. ♦ 12 0 0 | 24 0 0 0 | 8 6 0 0 0 0 0 | * 160 * * * * * ♦ 0 3 0 1 0 0 0 | 0 3 0 3 0 0 0 | 1 0 3 0 0 ... ... ... oo.3xo. ...&#x ♦ 3 1 0 | 3 3 0 0 | 1 0 3 0 0 0 0 | * * 1280 * * * * | 0 0 3 1 0 0 0 | 0 0 3 3 0 0 0 | 0 1 3 0 0 ... ... ... ... xox4oqo&#xt ♦ 4 4 4 | 4 8 8 4 | 0 1 4 4 4 0 1 | * * * 240 * * * ♦ 0 0 0 4 0 0 0 | 0 0 0 6 0 0 0 | 0 0 4 0 0 ... ... ... .oo3.ox ...&#x ♦ 0 1 3 | 0 0 3 3 | 0 0 0 0 3 1 0 | * * * * 1280 * * | 0 0 0 1 3 0 0 | 0 0 0 3 3 0 0 | 0 0 3 1 0 ... ... ..o3..o3..x ... ♦ 0 0 4 | 0 0 0 6 | 0 0 0 0 0 4 0 | * * * * * 960 * | 0 0 0 0 1 2 1 | 0 0 0 1 2 1 2 | 0 0 2 1 1 ... ... ... ..o3..x4..o ♦ 0 0 12 | 0 0 0 24 | 0 0 0 0 0 8 6 | * * * * * * 160 ♦ 0 0 0 1 0 0 3 | 0 0 0 3 0 0 3 | 0 0 3 0 1 ----------------------------+------------+-----------------+-------------------------------+-------------------------------+---------------------------+------------------------+------------- ... o..3o..3o..3x.. ... ♦ 5 0 0 | 10 0 0 0 | 10 0 0 0 0 0 0 | 5 0 0 0 0 0 0 | 384 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 0 ... ... o..3o..3x..4o.. ♦ 32 0 0 | 96 0 0 0 | 64 24 0 0 0 0 0 | 16 8 0 0 0 0 0 | * 60 * * * * * | 0 2 0 1 0 0 0 | 1 0 2 0 0 ... ... oo.3oo.3xo. ...&#x ♦ 4 1 0 | 6 4 0 0 | 4 0 6 0 0 0 0 | 1 0 4 0 0 0 0 | * * 960 * * * * | 0 0 2 1 0 0 0 | 0 1 2 0 0 ... ... ... ooo3xox4oqo&#xt ♦ 12 8 12 | 24 24 24 24 | 8 6 24 12 24 8 6 | 0 1 8 6 8 0 1 | * * * 160 * * * | 0 0 0 3 0 0 0 | 0 0 3 0 0 ... ... .oo3.oo3.ox ...&#x ♦ 0 1 4 | 0 0 4 6 | 0 0 0 0 6 4 0 | 0 0 0 0 4 1 0 | * * * * 960 * * | 0 0 0 1 2 0 0 | 0 0 2 1 0 ... ..o3..o3..o3..x ... ♦ 0 0 5 | 0 0 0 10 | 0 0 0 0 0 10 0 | 0 0 0 0 0 5 0 | * * * * * 384 * | 0 0 0 0 1 1 1 | 0 0 1 1 1 ... ... ..o3..o3..x4..o ♦ 0 0 32 | 0 0 0 96 | 0 0 0 0 0 64 24 | 0 0 0 0 0 16 8 | * * * * * * 60 | 0 0 0 1 0 0 2 | 0 0 2 0 1 ----------------------------+------------+-----------------+-------------------------------+-------------------------------+---------------------------+------------------------+------------- o..3o..3o..3o..3x.. ... ♦ 6 0 0 | 15 0 0 0 | 20 0 0 0 0 0 0 | 15 0 0 0 0 0 0 | 6 0 0 0 0 0 0 | 64 * * * * * * | 1 1 0 0 0 ... o..3o..3o..3x..4o.. ♦ 80 0 0 | 320 0 0 0 | 320 80 0 0 0 0 0 | 160 40 0 0 0 0 0 | 32 10 0 0 0 0 0 | * 12 * * * * * | 1 0 1 0 0 ... oo.3oo.3oo.3xo. ...&#x ♦ 5 1 0 | 10 5 0 0 | 10 0 10 0 0 0 0 | 5 0 10 0 0 0 0 | 1 0 5 0 0 0 0 | * * 384 * * * * | 0 1 1 0 0 ... ... ooo3ooo3xox4oqo&#xt ♦ 32 16 32 | 96 64 64 96 | 64 24 96 32 96 64 24 | 16 8 64 24 64 16 8 | 0 1 16 8 16 0 1 | * * * 60 * * * | 0 0 2 0 0 ... .oo3.oo3.oo3.ox ...&#x ♦ 0 1 5 | 0 0 5 10 | 0 0 0 0 10 10 0 | 0 0 0 0 10 5 0 | 0 0 0 0 5 1 0 | * * * * 384 * * | 0 0 1 1 0 ..o3..o3..o3..o3..x ... ♦ 0 0 6 | 0 0 0 15 | 0 0 0 0 0 20 0 | 0 0 0 0 0 15 0 | 0 0 0 0 0 6 0 | * * * * * 64 * | 0 0 0 1 1 ... ..o3..o3..o3..x4..o ♦ 0 0 80 | 0 0 0 320 | 0 0 0 0 0 320 80 | 0 0 0 0 0 160 40 | 0 0 0 0 0 32 10 | * * * * * * 12 | 0 0 1 0 1 ----------------------------+------------+-----------------+-------------------------------+-------------------------------+---------------------------+------------------------+------------- o..3o..3o..3o..3x..4o.. ♦ 192 0 0 | 960 0 0 0 | 1280 240 0 0 0 0 0 | 960 160 0 0 0 0 0 | 384 60 0 0 0 0 0 | 64 12 0 0 0 0 0 | 1 * * * * oo.3oo.3oo.3oo.3xo. ...&#x ♦ 6 1 0 | 15 6 0 0 | 20 0 15 0 0 0 0 | 15 0 20 0 0 0 0 | 6 0 15 0 0 0 0 | 1 0 6 0 0 0 0 | * 64 * * * ... ooo3ooo3ooo3xox4oqo&#xt ♦ 80 32 80 | 320 160 160 320 | 320 80 320 80 320 320 80 | 160 40 320 80 320 160 40 | 32 10 160 40 160 32 10 | 0 1 32 10 32 0 1 | * * 12 * * .oo3.oo3.oo3.oo3.ox ...&#x ♦ 0 1 6 | 0 0 6 15 | 0 0 0 0 15 20 0 | 0 0 0 0 20 15 0 | 0 0 0 0 15 6 0 | 0 0 0 0 6 1 0 | * * * 64 * ..o3..o3..o3..o3..x4..o ♦ 0 0 192 | 0 0 0 960 | 0 0 0 0 0 1280 240 | 0 0 0 0 0 960 160 | 0 0 0 0 0 384 60 | 0 0 0 0 0 64 12 | * * * * 1
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