Tier: First
Computation: 6 segments
Area of Effect: Synthesized item
Range: Touch
Duration: 6 rounds + 2 rounds per level
Glass Required: No
B-M-S Cost: 1.5
This function creates a temporary geometric weapon whose blade is but two dimensions. Because of the thinness of the nearly invisible cutting edge, the blade inflicts impressive damage. While the weapon speed and parry attributes are unmodified, the weapon inflicts 1d4+6 damage due to its sharpness. This weapon inflicts triple damage against geometric constructions (such as Geometric Shield, Sphere, Staircase, etc.) as well as triple damage against Constructs. For Monofilament weapons, if the Mathematician is not proficient in the weapon type (in this case, if he is not proficient in dagger), he may still use the weapon and suffer only on half of the BAtCh penalty for weapon unfamiliarity. Because the dagger constitutes a magical/enhanced weapon, the device functions at +1 to BAtCh for every three levels of the Mathematician, and is cumulative with any proficiency that the wielder possesses.
Tier: Second
Computation: 9 segments
Area of Effect: Synthesized Item
Range: Line of Sight, RTT
Duration: One round per level
Glass Required: No
B-M-S Cost: 1.25
This function creates a throwing star of great range and accurate return. Upon impact, the base damage is 1d6 against non-living targets, 1d6+3 versus flesh, and 2d6+3 against geometric spells and Constructs. Added to that damage is 1 point per level of the Mathematician. The weapon travels at 64// with MC(A) and is targeted by using a Ranged Touch Attack against the intended victim. If the target is missed, the weapon disappears and then reforms in the Mathematician's hand at the end of the round in which it was launched. The weapon has an initiative delay of 1.
By completing this function, a whip of one particle thickness is created. The whip inflicts 2d6 damage against flesh, and 3d6+3 against Geometric/Construct targets. On a critical success against flesh or against an anthropomorphic Construct, the target must make a save versus magical weapon or have to take a roll on the "dreadful wounding" chart. The weapon's BAtCh bonuses are identical to the Monofilament Dagger. Its speed and range is equivalent to a bull whip.
Tier: Fourth
Computation: 1 round
Area of Effect: Synthesized Item
Range: Touch
Duration: 3 rounds + 1 round per level
Glass Required: No
B-M-S Cost: 2.5
This particularly grim weapon inflicts 3d6 damage versus living/normal targets, and 5d6 against Geometric/Construct targets. Moreover, each round the rapier can launch a monofilament projectile that inflicts 2d6 versus normal/living and 3d6 versus Geometric/Constructs. The projectile's ranges are PB(3//), NR(8//), LR(14//), and ER(20//). The rapier has one projectile per two levels of the Mathematician. Like all Monofilament weapons, the BAtCh bonus increases as the character advances in levels (see Monofilament Dagger.)
The ultimate monofilament weapon, the Rift Sword spells utter disaster for any foe. Once this formula is used, a spectral sword woven of the darkest night appears a few feet away from the Mathematician. The blade of the weapon is actually a dimensional rift and thus has deadly effects upon its victims. It functions as a +5 consecrated weapon and deals 2d12 points of damage. Anyone struck by the Rift Sword must also make a Save vs. Magical weapon (with a +4) bonus or be disintegrated.
The sword can fly at a movement rate of 20, has a maneuverability rating of B, and is completely under the control of the caster. The weapon attacks on the Mathematician's initiative round and has a BAtCh equal to that of a Warrior of one half of the current level of the Mathematician. The summoned weapon has 5 Structural Points and an armour class of 2. Additionally, only energy attacks, spiritual powers, or other consecrated or magical weapons can harm it.
The weapon is under the direct control of the Mathematician, but it can function independently as well. If left alone, it will strike out at whatever target appears to be the greatest threat to the Mathematician and will act with the intelligence of a reasonably smart dog. However, the Mathematician may at any time give the weapon a command of around one sentence in length, and it will obey without question. Giving a command does require much time or concentration and can be done even if bound, injured, or otherwise distracted.
Other notes on the Rift Sword: Since it is not alive, the weapon is immune to Charm/Sleep effects, as well as certain other forms of magic and spiritual powers that only affect the living. If the Sword leaves the area of effect, it disappears.